On tensor categories attached to cells in affine Weyl groups II

2001/02/28 by Roman Bezrukavnikov, Bezrukavnikov, Roman, Viktor Ostrik +1
Mathematics · Medicine · #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/0102220

14 pages

arxiv created 2001/02/28 · openalex publication_date 2001/02/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

George Lusztig conjectured that asymptotic affine Hecke algebra of a simply connected group can be explicitly described in terms of convolution algebras. Main Theorem of this note (which is a continuation of RT/0010089) is a weak version of this Conjecture. This version is strong enough to reprove all previously known results (due to Nanhua Xi) in this direction, for example the case of type A_n, see QA/0010159.

Related

• On tensor categories attached to cells in affine Weyl groups, III
• Tensor categories attached to exceptional cells in Weyl groups
• The based ring of the lowest two-sided cell of an affine Weyl group, III
• A geometric realization of the asymptotic affine Hecke algebra
• Asymptotic Hecke algebras and involutions