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Algebraic Groups and Quantum Groups
 
Edited by: 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
Algebraic Groups and Quantum Groups
eBook ISBN:  978-0-8218-8536-9
Product Code:  CONM/565.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Algebraic Groups and Quantum Groups
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Algebraic Groups and Quantum Groups
Edited by: 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
eBook ISBN:  978-0-8218-8536-9
Product Code:  CONM/565.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 5652012; 286 pp
    MSC: Primary 05; 16; 17; 20; 81

    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.

    Readership

    Graduate students and research mathematicians interested in representation theory, combinatorics, group theory, number theory, and mathematical physics.

  • Table of Contents
     
     
    • Articles
    • 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 $\mathcal {O}$ 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 $G_1T$-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 $A$, Part I: Construction of the affine analogs
    • Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito — Toward Berenstein-Zelevinsky data in affine type $A$, 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 $E_6^{(1)}$
    • Toshiaki Shoji and Nanhua Xi — Iwahori’s question for affine Hecke algebras
    • Kentaro Wada — On Weyl modules of cyclotomic $q$-Schur algebras
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 5652012; 286 pp
MSC: Primary 05; 16; 17; 20; 81

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.

Readership

Graduate students and research mathematicians interested in representation theory, combinatorics, group theory, number theory, and mathematical physics.

  • Articles
  • 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 $\mathcal {O}$ 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 $G_1T$-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 $A$, Part I: Construction of the affine analogs
  • Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito — Toward Berenstein-Zelevinsky data in affine type $A$, 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 $E_6^{(1)}$
  • Toshiaki Shoji and Nanhua Xi — Iwahori’s question for affine Hecke algebras
  • Kentaro Wada — On Weyl modules of cyclotomic $q$-Schur algebras
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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