Representations of affine Hecke algebras

DOI10.1007/BFb0074130zbMath0817.20051MaRDI QIDQ1337749

Nanhua Xi

Publication date: 10 November 1994

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

algebraic groupsaffine Weyl groupsvector bundlessimple modulesrepresentation theoryaffine Hecke algebrasconnected reductive groupsbased ringsextended affine Weyl groupscharacter groupsasymptotic Hecke algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representation theory for linear algebraic groups (20G05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Algebraic (K)-theory and (L)-theory (category-theoretic aspects) (18F25) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

Related Items (31)

The Steinberg variety and representations of reductive groups. ⋮ On generalized cells in affine Weyl groups ⋮ Hecke algebras for \(\mathrm{GL}_n\) over local fields ⋮ Some translations in the second lowest two-sided cell of an affine Weyl group ⋮ Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group ⋮ Isomorphisms between affine Hecke algebras of type \(\widetilde{A_2}\). ⋮ Kazhdan-Lusztig basis and a geometric filtration of an affine Hecke algebra. II. ⋮ Cells in modified \(\imath\)quantum groups of type AIII and related Schur algebras ⋮ The based rings of two-sided cells in an affine Weyl group of type \(\tilde{B}_3\). I ⋮ Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type \(\widetilde A_n\). ⋮ Representations of rank two affine Hecke algebras at roots of unity. ⋮ A classification of commutative parabolic Hecke algebras. ⋮ Morita equivalence for $k$-algebras ⋮ Cellularity of the lowest two-sided ideal of an affine Hecke algebra. ⋮ Conjectures P1--P15 for Coxeter groups with complete graph ⋮ Global crystal bases for integrable modules over a quantum symmetric pair of type AIII ⋮ On representations of affine Hecke algebras of type \(B\). ⋮ On the determination of Kazhdan-Lusztig cells for affine Weyl groups with unequal parameters. ⋮ The based ring of the lowest two-sided cell of an affine Weyl group. III ⋮ The based ring of the lowest generalized two-sided cell of an extended affine Weyl group ⋮ Unnamed Item ⋮ A partition of the Springer fibers \({\mathcal B}_N\) for type \(A_{n-1}\), \(B_2\), \(G_2\) and some applications ⋮ Kazhdan-Lusztig coefficients for an affine Weyl group of type \(\widetilde B_2\). ⋮ The classification of elements in \(T\times\mathbb{C}^*\). ⋮ A Local Limit Theorem for Random Walks on the Chambers of Ã2 Buildings ⋮ Generalized induction of Kazhdan-Lusztig cells. ⋮ Diagram algebras, Hecke algebras and decomposition numbers at roots of unity ⋮ Stratifying endomorphism algebras associated to Hecke algebras ⋮ Affine quantum Schur algebras at roots of unity ⋮ On relations between the classical and the Kazhdan-Lusztig representations of symmetric groups and associated Hecke algebras. ⋮ Affine Hecke algebras and generalized standard Young tableaux.

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