Canonical left cells in affine Weyl groups

DOI10.1016/0001-8708(88)90031-XzbMath0664.20028MaRDI QIDQ1115531

Nanhua Xi, George Lusztig

Publication date: 1988

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

left cellstwo-sided cellCoxeter generatorsspecial elementirreducible affine Weyl group

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Representation theory for linear algebraic groups (20G05) Other geometric groups, including crystallographic groups (20H15)

Related Items (24)

On tensor categories attached to cells in affine Weyl groups. III. ⋮ Calculating Canonical Distinguished Involutions in the Affine Weyl Groups ⋮ Two-sided cells in type \(B\) (asymptotic case). ⋮ Cells in affine Weyl groups and tensor categories ⋮ The based ring of the lowest two-sided cell of an affine Weyl group. II ⋮ Cell decomposition in the affine weyl group w_A([Btilde₄)] ⋮ Some left cells in the affine Weyl group Ẽ₆ ⋮ Left cells witha-value 4 in the affine weyl group of type[btilde_n] ⋮ Tensor ideals in the category of tilting modules ⋮ Cells and \(q\)-Schur algebras ⋮ Left cells in the affine Weyl group of type \(\widetilde F_4\) ⋮ On the structure of the affine asymptotic Hecke algebras ⋮ Co-𝑡-structures on derived categories of coherent sheaves and the cohomology of tilting modules ⋮ Left Cells witha-Value 4 in the Affine Weyl Groups (i = 6, 7, 8) ⋮ A counterpart of the Verlinde algebra for the small quantum group. ⋮ The based ring of the lowest two-sided cell of an affine Weyl group ⋮ The second lowest two-sided cell in an affine Weyl group. ⋮ Support varieties for quantum groups ⋮ Billiards and tilting characters for \(\mathrm{SL}_3\) ⋮ On support varieties and the Humphreys conjecture in type \(A\) ⋮ Left cells in the affine Weyl group of type \(\widetilde C_4\) ⋮ $C^{-\infty}$-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations ⋮ Analogues of Weyl's Formula for Reduced Enveloping Algebras ⋮ On the Humphreys conjecture on support varieties of tilting modules

Cites Work

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• Cells in affine Weyl groups. II
• Representations of Coxeter groups and Hecke algebras
• A Two-Sided Cell in an Affine Weyl Group
• A Two-Sided Cell in an Affine Weyl Group, II

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