Algebraic Groups and Quantum Groups
About this Title
Susumu Ariki, Osaka University, Osaka, Japan, Hiraku Nakajima, Kyoto University, Kyoto, Japan, Yoshihisa Saito, University of Tokyo, Tokyo, Japan, Ken-ichi Shinoda, Sophia University, Tokyo, Japan, Toshiaki Shoji, Nagoya University, Nagoya, Japan, Toshiyuki Tanisaki, Osaka City University, Osaka, Japan, Susumu Ariki, Osaka University, Osaka, Japan, Hiraku Nakajima, Kyoto University, Kyoto, Japan, Yoshihisa Saito, University of Tokyo, Tokyo, Japan, Ken-ichi Shinoda, Sophia University, Tokyo, Japan, Toshiaki Shoji, Nagoya University, Nagoya, Japan and Toshiyuki Tanisaki, Osaka City University, Osaka, Japan, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 565
ISBNs: 978-0-8218-5317-7 (print); 978-0-8218-8536-9 (online)
This volume contains the proceedings of the tenth international conference on Representation Theory of Algebraic Groups and Quantum Groups, held August 2–6, 2010, at Nagoya University, Nagoya, Japan.
The survey articles and original papers contained in this volume offer a comprehensive view of current developments in the field. Among others reflecting recent trends, one central theme is research on representations in the affine case. In three articles, the authors study representations of W-algebras and affine Lie algebras at the critical level, and three other articles are related to crystals in the affine case, that is, Mirkovic–Vilonen polytopes for affine type $A$ and Kerov-Kirillov-Reshetikhin type bijection for affine type $E_6$.
Other contributions cover a variety of topics such as modular representation theory of finite groups of Lie type, quantum queer super Lie algebras, Khovanov's arc algebra, Hecke algebras and cyclotomic $q$-Schur algebras, $G_1T$-Verma modules for reductive algebraic groups, equivariant $K$-theory of quantum vector bundles, and the cluster algebra.
This book is suitable for graduate students and researchers interested in geometric and combinatorial representation theory, and other related fields.
Graduate students and research mathematicians interested in representation theory, combinatorics, group theory, number theory, and mathematical physics.
Table of Contents
- Tomoyuki Arakawa – W-algebras at the critical level
- Roman Bezrukavnikov and Qian Lin – Highest weight modules at the critical level and noncommutative Springer resolution
- Jonathan Brundan – An orthogonal form for level two Hecke algebras with applications
- Peter Fiebig – On the restricted projective objects in the affine category at the critical level
- Meinolf Geck – Remarks on modular representations of finite groups of Lie type in non-defining characteristic
- Ji Hye Jung and Seok-Jin Kang – Quantum queer superalgebras
- Masaharu Kaneda – Homomorphisms between neighboring -Verma modules
- G. I. Lehrer and R. B. Zhang – Quantum group actions on rings and equivariant K-theory
- Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito – Toward Berenstein-Zelevinsky data in affine type , Part I: Construction of the affine analogs
- Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito – Toward Berenstein-Zelevinsky data in affine type , Part II: Explicit description
- Tomoki Nakanishi and Andrei Zelevinsky – On tropical dualities in cluster algebras
- Masato Okado and Nobumasa Sano – KKR type bijection for the exceptional affine algebra
- Toshiaki Shoji and Nanhua Xi – Iwahori's question for affine Hecke algebras
- Kentaro Wada – On Weyl modules of cyclotomic -Schur algebras