## Representation theory of algebraic groups and quantum groupsThis 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, tensorcategories 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, Greenfunctions 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. |

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### Contents

Henning Haahr ANDERSEN Cells in affine Weyl groups and tilting | 1 |

Susumu ARIKI and Andrew Mathas Heche algebras with a finite | 17 |

Sergey Arkhipov Algebraic construction of contragradient quasi | 27 |

Copyright | |

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### Other editions - View all

Representation Theory of Algebraic Groups and Quantum Groups Akihiko Gyoja,Hiraku Nakajima,Ken-Ichi Shinoda No preview available - 2011 |

### Common terms and phrases

action affine Hecke algebra affine Weyl group Algebraic Groups algebras of type Ariki Ariki-Koike algebras assume automorphism basis bijection canonical Cartan character cohomology combinatorial commutative complex complex reflection groups conjecture consider contragradient Corollary corresponding crystal base crystal graph decomposition define definition denote diagram elements equation equivalent filtration finite dimensional follows formula functions functor g-module g-Schur Grothendieck group Hence highest weight homomorphism implies integral involution irreducible representations isomorphism Kashiwara Lemma Lie algebra linear Lusztig Math matrix minor determinants modular monoidal category multipartition nilpotent nonintersecting paths notation obtain orbit polynomials Proof Proposition proved quantum affine algebras quantum groups quotient Remark representation theory representation type resp result root of unity semisimple sheaves simple modules space Specht modules structure subalgebra subgroup submodule summand symmetric group tableaux Theorem tilting modules tropical unipotent unique Ux(g vector Verma module weight cell weight module Young wall