eBook ISBN:  9780821885369 
Product Code:  CONM/565.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821885369 
Product Code:  CONM/565.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 565; 2012; 286 ppMSC: 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 Walgebras 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 KerovKirillovReshetikhin 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.
ReadershipGraduate students and research mathematicians interested in representation theory, combinatorics, group theory, number theory, and mathematical physics.

Table of Contents

Articles

Tomoyuki Arakawa — Walgebras 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 nondefining characteristic

Ji Hye Jung and SeokJin 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 Ktheory

Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito — Toward BerensteinZelevinsky data in affine type $A$, Part I: Construction of the affine analogs

Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito — Toward BerensteinZelevinsky 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


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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 Walgebras 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 KerovKirillovReshetikhin 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.

Articles

Tomoyuki Arakawa — Walgebras 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 nondefining characteristic

Ji Hye Jung and SeokJin 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 Ktheory

Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito — Toward BerensteinZelevinsky data in affine type $A$, Part I: Construction of the affine analogs

Satoshi Naito, Daisuke Sagaki and Yoshihisa Saito — Toward BerensteinZelevinsky 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