The based ring of the lowest two-sided cell of an affine Weyl group

DOI10.1016/0021-8693(90)90059-WzbMath0709.20021MaRDI QIDQ921118

Nanhua Xi

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

Grothendieck groupaffine Weyl groupmaximal torusroot latticetwo-sided cellbased ringcategory of G-equivariant complex vector bundlesG-setsimply connected, almost simple complex algebraic group

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Grothendieck groups (category-theoretic aspects) (18F30)

Related Items

Geometric structure in the principal series of the 𝑝-adic group 𝐺₂ ⋮ Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group ⋮ The based ring of the lowest two-sided cell of an affine Weyl group. II ⋮ Subalgebras of the Fomin-Kirillov algebra ⋮ The lowest two-sided cell of a Coxeter group with complete graph ⋮ Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type \(\widetilde A_n\). ⋮ Cyclage, catabolism, and the affine Hecke algebra. ⋮ Conjectures P1--P15 for Coxeter groups with complete graph ⋮ Decomposition for Kazhdan-Lusztig basis elements of the affine Hecke algebra of type \(\tilde{A}_{n - 1}\) ⋮ 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

Cites Work

• Unnamed Item
• Canonical left cells in affine Weyl groups
• Hecke algebras and Jantzen's generic decomposition patterns
• Representations of Coxeter groups and Hecke algebras
• Distinguished conjugacy classes and elliptic Weyl group elements
• A Two-Sided Cell in an Affine Weyl Group, II