Traces on Iwahori-Hecke algebras and counting rational points

2021/05/10 by G. Lusztig, Lusztig, G. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2105.04061

openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let w be an element of the Weyl group of a reductive group G defined and split over a finite field. We consider the variety of triples (g,B,B') where g is a unipotent element of G and B, B' are Borel subgroups of G such that B contains g and B',gB'g^-1 are in relative position w. We show that the number of rational points of this variety can be expressed in terms of a trace on the Iwahori-Hecke algebra. We also show that this variety is smooth, irreducible, if w is elliptic, of minimal length in its conjugacy class.

Citations

• From conjugacy classes in the Weyl group to representations
• Two partitions of a flag manifold

Cited by

• From the Hecke Category to the Unipotent Locus

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