Gelfand Triples And Their Hecke Algebras

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Gelfand Triples and Their Hecke Algebras

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Nature
ISBN 13 : 3030516075
Total Pages : 153 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Gelfand Triples and Their Hecke Algebras by : Tullio Ceccherini-Silberstein

Download or read book Gelfand Triples and Their Hecke Algebras written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2020-09-25 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.

Groups and Graphs, Designs and Dynamics

Author : R. A. Bailey
Publisher : Cambridge University Press
ISBN 13 : 1009465945
Total Pages : 452 pages
Book Rating : 4.0/5 (94 download)

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Book Synopsis Groups and Graphs, Designs and Dynamics by : R. A. Bailey

Download or read book Groups and Graphs, Designs and Dynamics written by R. A. Bailey and published by Cambridge University Press. This book was released on 2024-05-30 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

Double Affine Hecke Algebras

Author : Ivan Cherednik
Publisher : Cambridge University Press
ISBN 13 : 9781139441254
Total Pages : 452 pages
Book Rating : 4.4/5 (412 download)

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Book Synopsis Double Affine Hecke Algebras by : Ivan Cherednik

Download or read book Double Affine Hecke Algebras written by Ivan Cherednik and published by Cambridge University Press. This book was released on 2005-03-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, for those who want to master the double Hecke algebra technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter 0 and selected topics from other chapters.

Discrete Harmonic Analysis

Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
ISBN 13 : 1316863654
Total Pages : 589 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis Discrete Harmonic Analysis by : Tullio Ceccherini-Silberstein

Download or read book Discrete Harmonic Analysis written by Tullio Ceccherini-Silberstein and published by Cambridge University Press. This book was released on 2018-06-21 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.

Lie Groups

Author : Daniel Bump
Publisher : Springer Science & Business Media
ISBN 13 : 1461480248
Total Pages : 532 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Lie Groups by : Daniel Bump

Download or read book Lie Groups written by Daniel Bump and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

Infinite Analysis: Rims Project 1991 (In 2 Volumes)

Author : Tohru Eguchi
Publisher : World Scientific
ISBN 13 : 9814554901
Total Pages : 1104 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Infinite Analysis: Rims Project 1991 (In 2 Volumes) by : Tohru Eguchi

Download or read book Infinite Analysis: Rims Project 1991 (In 2 Volumes) written by Tohru Eguchi and published by World Scientific. This book was released on 1992-06-25 with total page 1104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of original research papers presented at the workshop. The main topics covered are Conformal Field Theory, Integrable Massive Field Theory, Quantum Gravity, Quantum Group, Lattice Solvable Models, Low Dimensional Topology, and C* Algebras.

Unipotent Hecke Algebras

Author : F. Nathaniel Edgar Thiem
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Unipotent Hecke Algebras by : F. Nathaniel Edgar Thiem

Download or read book Unipotent Hecke Algebras written by F. Nathaniel Edgar Thiem and published by . This book was released on 2004 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectra of Symmetrized Shuffling Operators

Author : Victor Reiner
Publisher : American Mathematical Soc.
ISBN 13 : 0821890956
Total Pages : 121 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectra of Symmetrized Shuffling Operators by : Victor Reiner

Download or read book Spectra of Symmetrized Shuffling Operators written by Victor Reiner and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of O -noninversions of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.

Lie Algebras and Related Topics

Author : Georgia Benkart
Publisher : American Mathematical Soc.
ISBN 13 : 0821851195
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Algebras and Related Topics by : Georgia Benkart

Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.

Encyclopaedia of Mathematics, Supplement III

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 0306483734
Total Pages : 564 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Encyclopaedia of Mathematics, Supplement III by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics, Supplement III written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2007-11-23 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

The Unity of Mathematics

Author : Pavel Etingof
Publisher : Springer Science & Business Media
ISBN 13 : 0817644679
Total Pages : 646 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis The Unity of Mathematics by : Pavel Etingof

Download or read book The Unity of Mathematics written by Pavel Etingof and published by Springer Science & Business Media. This book was released on 2007-05-31 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tribute to the vision and legacy of Israel Moiseevich Gel'fand Written by leading mathematicians, these invited papers reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program

Quantum Groups and Their Primitive Ideals

Author : Anthony Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 3642784003
Total Pages : 394 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Quantum Groups and Their Primitive Ideals by : Anthony Joseph

Download or read book Quantum Groups and Their Primitive Ideals written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature.

I. M. Gelfand Seminar

Author : Izrailʹ Moiseevich Gelʹfand
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis I. M. Gelfand Seminar by : Izrailʹ Moiseevich Gelʹfand

Download or read book I. M. Gelfand Seminar written by Izrailʹ Moiseevich Gelʹfand and published by . This book was released on 1993 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

I. M. Gelfand Seminar, Parts 1 And 2

Author : Sergeĭ Izrailevich Gelʹfand
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 234 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis I. M. Gelfand Seminar, Parts 1 And 2 by : Sergeĭ Izrailevich Gelʹfand

Download or read book I. M. Gelfand Seminar, Parts 1 And 2 written by Sergeĭ Izrailevich Gelʹfand and published by American Mathematical Society(RI). This book was released on 1993 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers by participants in the celebrated seminar of I. M. Gelfand, which ran for more than forty years at Moscow State University. Among the authors are some of the world's most renowned mathematicians. The high scientific level of the articles makes this an important contribution to the literature.

Studies in Memory of Issai Schur

Author : Anthony Joseph
Publisher : Springer Science & Business Media
ISBN 13 : 1461200458
Total Pages : 545 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Studies in Memory of Issai Schur by : Anthony Joseph

Download or read book Studies in Memory of Issai Schur written by Anthony Joseph and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume Studies in Memory of Issai Schur was conceived as a tribute to Schur's of his tragic end. His impact on great contributions to mathematics and in remembrance of mathematicians Representation Theory alone was so great that a significant number of Researchers (TMR) Network, in the European Community Training and Mobility Orbits, Crystals and Representation Theory, in operation during the period (1997-2002) have been occupied with what has been called Schur theory. Consequently, this volume has the additional purpose of recording some of the significant results of the network. It was furthermore appropriate that invited contributors should be amongst the speakers at the Paris Midterm Workshop of the network held at Chevaleret during 21-25 May, 2000 as well as those of the Schur Memoriam Workshop held at the Weizmann Institute, Rehovot, during 27-31 December 2000. The latter marked the sixtieth anniversary of Schur's passing and took place in the 125th year of his birth.

Discrete Harmonic Analysis

Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
ISBN 13 : 1107182336
Total Pages : 589 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Discrete Harmonic Analysis by : Tullio Ceccherini-Silberstein

The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$

Author : Toshiyuki Kobayashi
Publisher : American Mathematical Soc.
ISBN 13 : 0821847570
Total Pages : 145 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ by : Toshiyuki Kobayashi

Download or read book The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ written by Toshiyuki Kobayashi and published by American Mathematical Soc.. This book was released on 2011 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on $\mathbb{R}^n$ ($n=n_1+n_2$: even). This transform is in some sense the unique and natural unitary operator on $L^2(C)$, as is the case with the Euclidean Fourier transform $\mathcal{F}_{\mathbb{R}^n}$ on $L^2(\mathbb{R}^n)$. Inspired by recent developments of algebraic representation theory of reductive groups, the authors shed new light on classical analysis on the one hand, and give the global formulas for the $L^2$-model of the minimal representation of the simple Lie group $G=O(n_1+1,n_2+1)$ on the other hand.