Title Algebraic groups and quantum groups : International Conference on Representation Theory of Algebraic Groups and Quantum Groups '10, August 2-6, 2010, Graduate School of Mathematics, Nagoya University, Nagoya, Japan / Susumu Ariki [and others], editors

Published Providence, R.I. : American Mathematical Society, ©2012

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Description 1 online resource (xi, 286 pages) : illustrations Series Contemporary mathematics ; 565 Contemporary mathematics (American Mathematical Society) ; v. 565. Contents Preface -- Program -- W-algebras at the critical level -- 1. Introduction -- 2. Associated graded vertex Poisson algebras -- 3. BRST cohomology of restricted Wakimoto modules -- 4. Proof of Theorems 1.1 and 1.2 -- References -- Highest weight modules at the critical level and noncommutative Springer resolution -- 1. Introduction -- 2. Noncommutative Springer resolution -- 3. Perverse sheaves on the affine flag variety -- 4. Results of Frenkel-Gaitsgory and a proof of Theorem 1 -- References -- An orthogonal form for level two Hecke algebras with applications 1. Introduction2. Level one Hecke algebras -- 3. Level two Hecke algebras -- 4. Khovanovâ€?s arc algebra -- 5. Category for Grassmannians -- 6. The general linear supergroup -- 7. The walled Brauer algebra -- References -- On the restricted projective objects in the affine category at the critical level -- 1. Introduction -- 2. Affine Kacâ€?Moody algebras -- 3. The deformed category -- 4. Projective objects in Ì? _{ } -- 5. Block decomposition of Ì? _{ } -- 6. The linkage principle -- References Remarks on modular representations of finite groups of Lie type in non-defining characteristic1. Introduction -- 2. On modular unipotent representations -- 3. Principal series representations -- 4. On the dimensions of irreducible representations -- References -- Quantum queer superalgebras -- Introduction -- 1. Queer Lie superalgebra () -- 2. Highest weight modules over () -- 3. Quantum queer superalgebra _{ }(()) -- 4. Representation Theory of _{ }(()) -- 5. Crystal Bases -- 6. Semistandard decomposition tableaux -- References Quantum group actions on rings and equivariant K-theory1. Introduction -- 2. Equivariant K-theory of quantum group actions -- 3. Categories of equivariant modules -- 4. Equivariant K-theory of filtered module algebras -- 5. Quantum symmetric algebras -- 6. Quantum homogeneous spaces -- Acknowledgements -- References -- Toward Berenstein-Zelevinsky data in affine type, Part I: Construction of the affine analogs -- 1. Introduction -- 2. Berenstein-Zelevinsky data of type _{ } -- 3. Berenstein-Zelevinsky data of type _{â?ž} 4. Berenstein-Zelevinsky data of type _{â??}â??¹â??5. Appendix -- References -- Toward Berenstein-Zelevinsky data in affine type, Part II: Explicit description -- 1. Introduction -- Acknowledgement -- 2. Review on Berenstein-Zelevinsky data associated to finite intervals -- 3. Berenstein-Zelevinsky data associated to â?? -- 4. Berenstein-Zelevinsky data of type _{ -1}â??¹â?? -- 5. Lusztig data of infinite size and a crystal structure on them -- 6. BZ data arising from Lusztig data of Infinite size Bibliography Includes bibliographical references Notes English Online resource; title from PDF title page (American Mathematical Society, viewed March 22, 2012) Subject Combinatorial group theory -- Congresses Representations of groups -- Congresses Combinatorial group theory Representations of groups Genre/Form Conference papers and proceedings Form Electronic book Author Ariki, Susumu, 1959- ISBN 9780821885369 0821885367

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