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Affine Hecke Algebras And Quantum Symmetric Pairs
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Book Synopsis Affine Hecke Algebras and Quantum Symmetric Pairs by : Zhaobing Fan
Download or read book Affine Hecke Algebras and Quantum Symmetric Pairs written by Zhaobing Fan and published by American Mathematical Society. This book was released on 2023-01-18 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Affine Flag Varieties and Quantum Symmetric Pairs by : Zhaobing Fan
Download or read book Affine Flag Varieties and Quantum Symmetric Pairs written by Zhaobing Fan and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum groups of finite and affine type $A$ admit geometric realizations in terms of partial flag varieties of finite and affine type $A$. Recently, the quantum group associated to partial flag varieties of finite type $B/C$ is shown to be a coideal subalgebra of the quantum group of finite type $A$.
Book Synopsis Twenty-Four Hours of Local Cohomology by : Srikanth B. Iyengar
Download or read book Twenty-Four Hours of Local Cohomology written by Srikanth B. Iyengar and published by American Mathematical Society. This book was released on 2022-07-19 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed to provide an introduction to local cohomology which takes cognizance of the breadth of its interactions with other areas of mathematics. It covers topics such as the number of defining equations of algebraic sets, connectedness properties of algebraic sets, connections to sheaf cohomology and to de Rham cohomology, Gröbner bases in the commutative setting as well as for $D$-modules, the Frobenius morphism and characteristic $p$ methods, finiteness properties of local cohomology modules, semigroup rings and polyhedral geometry, and hypergeometric systems arising from semigroups. The book begins with basic notions in geometry, sheaf theory, and homological algebra leading to the definition and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology, geometry, combinatorics, and algorithmic aspects of the subject.
Book Synopsis Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth by : Jie Du
Download or read book Forty Years Of Algebraic Groups, Algebraic Geometry, And Representation Theory In China: In Memory Of The Centenary Year Of Xihua Cao's Birth written by Jie Du and published by World Scientific. This book was released on 2022-10-21 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Xihua Cao (1920-2005) was a leading scholar at East China Normal University (ECNU) and a famous algebraist in China. His contribution to the Chinese academic circle is particularly the formation of a world-renowned 'ECNU School' in algebra, covering research areas include algebraic groups, quantum groups, algebraic geometry, Lie algebra, algebraic number theory, representation theory and other hot fields. In January 2020, in order to commemorate Professor Xihua Cao's centenary birthday, East China Normal University held a three-day academic conference. Scholars at home and abroad gave dedications or delivered lectures in the conference. This volume originates from the memorial conference, collecting the dedications of scholars, reminiscences of family members, and 16 academic articles written based on the lectures in the conference, covering a wide range of research hot topics in algebra. The book shows not only scholars' respect and memory for Professor Xihua Cao, but also the research achievements of Chinese scholars at home and abroad.
Book Synopsis Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification by : Jacob Greenstein
Download or read book Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification written by Jacob Greenstein and published by Springer Nature. This book was released on 2022-03-11 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
Book Synopsis Double Affine Hecke Algebras and Congruence Groups by : Bogdan Ion
Download or read book Double Affine Hecke Algebras and Congruence Groups written by Bogdan Ion and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by auto-morphisms of a finite index subgroup of the Artin group of type A2, which descends to a faithful outer action of a congruence subgroup of SL(2, Z)or PSL(2, Z). This was previously known only in some special cases and, to the best of our knowledge, not even conjectured to hold in full generality. It turns out that the structural intricacies of DAAG/DAHA are captured by the underlying semisimple data and, to a large extent, even by adjoint data; we prove our main result by reduction to the adjoint case. Adjoint DAAG/DAHA correspond in a natural way to affine Lie algebras, or more precisely to their affinized Weyl groups, which are the semi-direct products W Q∨ of the Weyl group W with the coroot lattice Q∨. They were defined topologically by van der Lek, and independently, algebraically, by Cherednik. We now describe our results for the adjoint case in greater detail. We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type A2,B2,G2 act by automorphisms on the adjoint DAAG/DAHA associated to affine Lie algebras of twist number r =1, 2, 3, respec-tively. This extends a fundamental result of Cherednik for r =1. We show further that the above rank two Artin group action descends to an outer action of the congruence subgroup Γ1(r). In particular, Γ1(r) acts naturally on the set of isomorphism classes of representations of an adjoint DAAG/DAHA of twist number r, giving rise to a projective representation of Γ1(r)on the spaceof aΓ1(r)-stable representation. We also provide a classification of the involutions of Kazhdan-Lusztig type that appear in the context of these actions.
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.
Book Synopsis Weight Multiplicities and Young Tableaux Through Affine Crystals by : Jang Soo Kim
Download or read book Weight Multiplicities and Young Tableaux Through Affine Crystals written by Jang Soo Kim and published by American Mathematical Society. This book was released on 2023-03-09 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Planar Algebras in Braided Tensor Categories by : André Gil Henriques
Download or read book Planar Algebras in Braided Tensor Categories written by André Gil Henriques and published by American Mathematical Society. This book was released on 2023-02-13 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Representation Theory of Geigle-Lenzing Complete Intersections by : Martin Herschend
Download or read book Representation Theory of Geigle-Lenzing Complete Intersections written by Martin Herschend and published by American Mathematical Society. This book was released on 2023-05-23 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract. https://www.ams.org/bookstore/pspdf/memo-285-1412-abstract.pdf?
Book Synopsis Congruence Lattices of Ideals in Categories and (Partial) Semigroups by : James East
Download or read book Congruence Lattices of Ideals in Categories and (Partial) Semigroups written by James East and published by American Mathematical Society. This book was released on 2023-04-07 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Twistors, Quartics,and del Pezzo Fibrations by : Nobuhiro Honda
Download or read book Twistors, Quartics,and del Pezzo Fibrations written by Nobuhiro Honda and published by American Mathematical Society. This book was released on 2023-05-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations by : Philipp Grohs
Download or read book A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations written by Philipp Grohs and published by American Mathematical Society. This book was released on 2023-04-07 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters by : Giao Ky Duong
Download or read book Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters written by Giao Ky Duong and published by American Mathematical Society. This book was released on 2023-05-23 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis On Pseudoconformal Blow-Up Solutions to the Self-Dual Chern-Simons-Schrödinger Equation: Existence, Uniqueness, and Instability by : Kihyun Kim
Download or read book On Pseudoconformal Blow-Up Solutions to the Self-Dual Chern-Simons-Schrödinger Equation: Existence, Uniqueness, and Instability written by Kihyun Kim and published by American Mathematical Society. This book was released on 2023-04-07 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity by : Nassif Ghoussoub
Download or read book Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity written by Nassif Ghoussoub and published by American Mathematical Society. This book was released on 2023-05-23 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Infinite Time Blow-Up Solutions to the Energy Critical Wave Maps Equation by : Mohandas Pillai
Download or read book Infinite Time Blow-Up Solutions to the Energy Critical Wave Maps Equation written by Mohandas Pillai and published by American Mathematical Society. This book was released on 2023-04-07 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
