Type A-admissible cells are Kazhdan-Lusztig

TL;DR

This paper proves that type A-admissible W-cells are indeed Kazhdan-Lusztig cells, confirming a conjecture and advancing the understanding of their role in Hecke algebra representations.

Contribution

It establishes that type A-admissible W-cells are Kazhdan-Lusztig cells, confirming a conjecture by Stembridge and linking combinatorial and algebraic structures.

Findings

Type A-admissible W-cells are Kazhdan-Lusztig cells

Confirms Stembridge's conjecture

Enhances understanding of Hecke algebra representations

Abstract

Admissible W-graphs were defined and combinatorially characterised by Stembridge in reference [12]. The theory of admissible W-graphs was motivated by the need to construct W-graphs for Kazhdan-Lusztig cells, which play an important role in the representation theory of Hecke algebras, without computing Kazhdan-Lusztig polynomials. In this paper, we shall show that type A-admissible W-cells are Kazhdan-Lusztig as conjectured by Stembridge in his original paper.