Representation Theory Of Algebraic Groups And Quantum Groups: (Advanced Studies in Pure Mathematics)

This book is a collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. It presents a comprehensive overview of developments in representation theory of algebraic groups and quantum groups. Particularly noteworthy are papers containing remarkable results concerning Lusztig's conjecture on cells in affine Weyl groups. The following topics were discussed: cells in affine Weyl groups, tilting modules, tensor categories attached to cells in affine Weyl groups, representations of algebraic groups in positive characteristic, representations of Hecke algebras, Ariki-Koike and cyclotomic $q$-Schur algebras, cellular algebras and diagram algebras, Gelfand-Graev representations of finite reductive groups, Green functions associated to complex reflection groups, induction theorem for Springer representations, representations of Lie algebras in positive characteristic, representations of quantum affine algebras, extremal weight modules, crystal bases, tropical Robinson-Schensted-Knuth correspondence and more. The material is suitable for graduate students and research mathematicians interested in representation theory of algebraic groups, Hecke algebras, quantum groups, and combinatorial theory. Information for our distributors: Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. All commercial channel discounts apply.

Table of Contents:
Cells in affine Weyl groups and tilting modules by H. H. Anderson Heche algebras with a finite number of indecomposable modules by S. Ariki and A. Mathas Algebraic construction of contragradient quasi-Verma modules in positive characteristic by S. Arkihopov On tensor categories attached to cells in affine Weyl groups by R. Bezrukavnikov Appendix: Braiding compatibilities by D. Gaitsgory On tensor categories attached to cells in affine Weyl groups II by R. Bezrukavnikov and V. Ostrik Zeta functions and functional equations associated with the components of the Gelfand-Graev representations of a finite reductive group by C. W. Curtis and K.-i. Shinoda Cellular algebras and diagram algebras in representation theory by J. J. Graham and G. I. Lehrer Representations of Lie algebras in positive characteristic by J. C. Jantzen Quantum affine algebras and crystal bases by S.-J. Kang An induction theorem for Springer's representations by G. Lusztig The representation theory of the Ariki-Koike and cyclotomic $q$-Schur algebras by A. Mathas Crystal bases and diagram automorphisms by S. Naito and D. Sagaki Extremal weight modules of quantum affine algebras by H. Nakajima Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions by M. Noumi and Y. Yamada Green functions attached to limit symbols by T. Shoji Cells for a Hecke algebra representation by T. A. Springer On the characterization of the set $\mathcal{D}_1$ of the affine Weyl group of type $\tilde{A}_n$ by N. Xi.