The Discrete Series of GLn Over a Finite Field

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Publisher : Princeton University Press
ISBN 13 : 9780691081540
Total Pages : 112 pages
Book Rating : 4.0/5 (815 download)

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Book Synopsis The Discrete Series of GLn Over a Finite Field by : George Lusztig

Download or read book The Discrete Series of GLn Over a Finite Field written by George Lusztig and published by Princeton University Press. This book was released on 1974-10-21 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes. The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).

The Discrete Series of GL(n) Over a Finite Field

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Publisher :
ISBN 13 :
Total Pages : 99 pages
Book Rating : 4.:/5 (797 download)

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Book Synopsis The Discrete Series of GL(n) Over a Finite Field by : George Lusztig

Download or read book The Discrete Series of GL(n) Over a Finite Field written by George Lusztig and published by . This book was released on 1974 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Discrete Series of GLn Over a Finite Field

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Publisher :
ISBN 13 : 9780691081458
Total Pages : 99 pages
Book Rating : 4.0/5 (814 download)

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Book Synopsis The Discrete Series of GLn Over a Finite Field by : George Lusztig

Download or read book The Discrete Series of GLn Over a Finite Field written by George Lusztig and published by . This book was released on 1940 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81

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Author :
Publisher : Princeton University Press
ISBN 13 : 1400881765
Total Pages : 104 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 by : George Lusztig

Download or read book Discrete Series of GLn Over a Finite Field. (AM-81), Volume 81 written by George Lusztig and published by Princeton University Press. This book was released on 2016-03-02 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes. The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq).

Group Theory

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Publisher : Springer
ISBN 13 : 3540397930
Total Pages : 409 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Group Theory by : Hsio-Fu Tuan

Download or read book Group Theory written by Hsio-Fu Tuan and published by Springer. This book was released on 2006-11-14 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Groups - Canberra 1989

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Publisher : Springer
ISBN 13 : 3540469001
Total Pages : 209 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Groups - Canberra 1989 by : L.G. Kovacs

Download or read book Groups - Canberra 1989 written by L.G. Kovacs and published by Springer. This book was released on 2006-12-08 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ischia Group Theory 2010

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Publisher : World Scientific
ISBN 13 : 9814350052
Total Pages : 416 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Ischia Group Theory 2010 by : Mariagrazia Bianchi

Download or read book Ischia Group Theory 2010 written by Mariagrazia Bianchi and published by World Scientific. This book was released on 2012 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Positive laws on generators in powerful pro-p groups / C. Acciarri and G.A. Fernandez-Alcober -- Periodic groups saturated by dihedral subgroups / B. Amberg and L. Kazarin -- A note on finite groups in which the conjugacy class sizes form an arithmetic progression / M. Bianchi, A. Gillio and P.P. Palfy -- A survey of recent progress on non-abelian tensor squares of groups / R.D. Blyth, F. Fumagalli and M. Morigi -- Conjugacy classes of subgroups of finite p-groups: the first gap / R. Brandl -- The Tutte polynomial of the Schreier graphs of the Grigorchuck group and the Basilica group / T. Ceccherini-Silberstein, A. Donno and D. Iacono -- On maximal subgroups of the alternating and symmetric groups / V. Colombo -- Markov's problems through the looking glass of Zariski and Markov topologies / D. Dikranjan and D. Toller -- Linear groups with finite dimensional orbits / M.R. Dixon, L.A. Kurdachenko and J. Otal -- Three-dimensional loops as sections in a four-dimensional solvable Lie group / A. Figula -- A note on finite p-groups with a maximal elementary subgroup of rank 2 / G. Glauberman -- Finitely generated free by C[symbol] pro-p groups / W. Herfort and P.A. Zalesskii -- Finite nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M[symbol] / Z. Janko -- Twisted conjugacy in certain Artin groups / A. Juhasz -- Applications of Clifford's theorem to Frobenius groups of automorphisms / E.I. Khukhro -- Inducing [symbol]-partial characters with a given vertex / M.L. Lewis -- Groups and Lie rings with Frobenius groups of automorphisms / N. Yu. Makarenko -- On integral representations of finite groups / D. Malinin -- On p-groups of small powerful class / A. Mann -- Lifting (2, k)-generators of linear groups / A. Maroti and C. Tamburini Bellani -- Fixed point subgroups and character tables / G. Navarro -- Permutability and seriality in locally finite groups / D.J.S. Robinson -- On the exponent of a finite group with a four-group of automorphisms / E. Romano and P. Shumyatsky -- Examples of Markov chains on spaces with multiplicities / F. Scarabotti and F. Tolli -- On the order and the element orders of finite groups: results and problems / W.J. Shi -- On local finiteness of verbal subgroups in residually finite groups / P. Shumyatsky -- The adjoint group of radical rings and related questions / Ya. P. Sysak -- On the Gorenstein dimension of soluble groups / O. Talelli -- Decomposition numbers for projective modules of finite Chevalley groups / A.E. Zalesski

Buildings

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Publisher : Springer Science & Business Media
ISBN 13 : 0387788352
Total Pages : 758 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Buildings by : Peter Abramenko

Download or read book Buildings written by Peter Abramenko and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher. This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

New Perspectives in Algebraic Combinatorics

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Publisher : Cambridge University Press
ISBN 13 : 9780521770873
Total Pages : 360 pages
Book Rating : 4.7/5 (78 download)

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Book Synopsis New Perspectives in Algebraic Combinatorics by : Louis J. Billera

Download or read book New Perspectives in Algebraic Combinatorics written by Louis J. Billera and published by Cambridge University Press. This book was released on 1999-09-28 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.

Representations and Cohomology: Volume 2, Cohomology of Groups and Modules

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Publisher : Cambridge University Press
ISBN 13 : 9780521636520
Total Pages : 296 pages
Book Rating : 4.6/5 (365 download)

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Book Synopsis Representations and Cohomology: Volume 2, Cohomology of Groups and Modules by : D. J. Benson

Download or read book Representations and Cohomology: Volume 2, Cohomology of Groups and Modules written by D. J. Benson and published by Cambridge University Press. This book was released on 1991-08-22 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: A further introduction to modern developments in the representation theory of finite groups and associative algebras.

Scissors Congruences, Group Homology & Characteristic Classes

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Publisher : World Scientific
ISBN 13 : 9814491837
Total Pages : 178 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Scissors Congruences, Group Homology & Characteristic Classes by : Johan L Dupont

Download or read book Scissors Congruences, Group Homology & Characteristic Classes written by Johan L Dupont and published by World Scientific. This book was released on 2001-02-26 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume “scissors-congruent”, i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.

Catalog of Copyright Entries. Third Series

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Publisher : Copyright Office, Library of Congress
ISBN 13 :
Total Pages : 1450 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Catalog of Copyright Entries. Third Series by : Library of Congress. Copyright Office

Download or read book Catalog of Copyright Entries. Third Series written by Library of Congress. Copyright Office and published by Copyright Office, Library of Congress. This book was released on 1976 with total page 1450 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Infinite Loop Spaces (AM-90), Volume 90

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Publisher : Princeton University Press
ISBN 13 : 1400821258
Total Pages : 230 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Infinite Loop Spaces (AM-90), Volume 90 by : John Frank Adams

Download or read book Infinite Loop Spaces (AM-90), Volume 90 written by John Frank Adams and published by Princeton University Press. This book was released on 1978-09-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.

Subgroup Complexes

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Publisher : American Mathematical Soc.
ISBN 13 : 0821805010
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Subgroup Complexes by : Stephen D. Smith

Download or read book Subgroup Complexes written by Stephen D. Smith and published by American Mathematical Soc.. This book was released on 2011-11-10 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an overview of a research area that combines geometries for groups (such as Tits buildings and generalizations), topological aspects of simplicial complexes from $p$-subgroups of a group (in the spirit of Brown, Quillen, and Webb), and combinatorics of partially ordered sets. The material is intended to serve as an advanced graduate-level text and partly as a general reference on the research area. The treatment offers optional tracks for the reader interested in buildings, geometries for sporadic simple groups, and $G$-equivariant equivalences and homology for subgroup complexes.

Harmonic Analysis, the Trace Formula, and Shimura Varieties

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821838440
Total Pages : 708 pages
Book Rating : 4.8/5 (384 download)

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Book Synopsis Harmonic Analysis, the Trace Formula, and Shimura Varieties by : Clay Mathematics Institute. Summer School

Download or read book Harmonic Analysis, the Trace Formula, and Shimura Varieties written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2005 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.

Reduction Theory and Arithmetic Groups

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Publisher : Cambridge University Press
ISBN 13 : 1108832032
Total Pages : 375 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Reduction Theory and Arithmetic Groups by : Joachim Schwermer

Download or read book Reduction Theory and Arithmetic Groups written by Joachim Schwermer and published by Cambridge University Press. This book was released on 2022-12-31 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Build a solid foundation in the area of arithmetic groups and explore its inherent geometric and number-theoretical components.

Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms

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Publisher : Springer
ISBN 13 : 3319952315
Total Pages : 367 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms by : Volker Heiermann

Download or read book Relative Aspects in Representation Theory, Langlands Functoriality and Automorphic Forms written by Volker Heiermann and published by Springer. This book was released on 2018-10-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a panorama of the diverse activities organized by V. Heiermann and D. Prasad in Marseille at the CIRM for the Chaire Morlet event during the first semester of 2016. It assembles together expository articles on topics which previously could only be found in research papers. Starting with a very detailed article by P. Baumann and S. Riche on the geometric Satake correspondence, the book continues with three introductory articles on distinguished representations due to P. Broussous, F. Murnaghan, and O. Offen; an expository article of I. Badulescu on the Jacquet–Langlands correspondence; a paper of J. Arthur on functoriality and the trace formula in the context of "Beyond Endoscopy", taken from the Simons Proceedings; an article of W-W. Li attempting to generalize Godement–Jacquet theory; and a research paper of C. Moeglin and D. Renard, applying the trace formula to the local Langlands classification for classical groups. The book should be of interest to students as well as professional researchers working in the broad area of number theory and representation theory.