TY  - BOOK
AU  - Ariki,Susumu
AU  - Nakajima,Hiraku
AU  - Saito,Yoshihisa
AU  - Shinoda,Ken-Ichi
AU  - Shoji,Toshiaki
TI  - Algebraic Groups and Quantum Groups
T2  - Contemporary Mathematics
SN  - 9780821885369
AV  - QA182.5 -- .I58 2010eb 
U1  - 512/.2 
PY  - 2012///
CY  - Providence
PB  - American Mathematical Society
KW  - Combinatorial group theory -- Congresses
KW  - Representations of groups -- Congresses
KW  - Electronic books
N1  - Intro -- 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. Introduction -- 2. Level one Hecke algebras -- 3. Level two Hecke algebras -- 4. Khovanov'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 Kac-Moody algebras -- 3. The deformed category -- 4. Projective objects in ̂  _{  } -- 5. Block decomposition of ̂  _{  } -- 6. The linkage principle -- References -- Remarks on modular representations of finite groups of Lie type in non-defining characteristic -- 1. 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-theory -- 1. 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   _{∞} -- 4. Berenstein-Zelevinsky data of type   _{ℓ}⁽¹⁾ -- 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 ℤ -- 4. Berenstein-Zelevinsky data of type   _{  -1}⁽¹⁾ -- 5. Lusztig data of infinite size and a crystal structure on them -- 6. BZ data arising from Lusztig data of Infinite size -- OT1OT1cmrcmrmmnnmbxAppendix A. Another explicit description -- References -- On tropical dualities in cluster algebras -- 1. Introduction -- 2. Proofs of Proposition 1.3 and identity (1.11) -- 3. Proofs of Proposition 1.4 and identity (1.12) -- 4. Some corollaries -- References -- KKR type bijection for the exceptional affine algebra   ₆⁽¹⁾ -- 1. Introduction -- 2. Quantum affine algebra and crystal -- 3. Rigged configuration and the bijection -- 4. The bijection -- 5. Proof of Theorem 4 -- References -- Iwahori's question for affine Hecke algebras -- 1. Affine Hecke algebras -- 2. Group algebra ℂ[  ] of -- 3. Some particular semisimple elements in -- Proof of Theorem 1.2 -- References -- On Weyl modules of cyclotomic   -Schur algebras -- 0. Introduction -- 1. Review on cyclotomic   -Schur algebras -- 2.   _{  }(  )-crystal structure on Weyl module   (  ) of   _{  ,  } -- 3. Some properties of the number   _{    } -- 4. Characters of the Weyl modules and symmetric functions -- 5. Decomposition matrices of cyclotomic   -Schur algebras; 6. The Ariki-Koike algebra as a subalgebra of   _{  ,  } -- References
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ER  -