Type \(A\) admissible cells are Kazhdan–Lusztig

Van Minh Nguyen

Abstract

Admissible \(W\!\)-graphs were defined and combinatorially characterised by Stembridge in A finiteness theorem for \(W\!\)-Graphs (Adv. Math. 229 (2012)). 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 show that type \(A\) admissible \(W\!\)-cells are Kazhdan–Lusztig, as conjectured by Stembridge in his original paper.

Keywords: Coxeter group, Hecke algebra, W-graph, cell.

AMS Subject Classification: Primary 20C08; secondary 20C30.