## 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.

: Primary 20C08; secondary 20C30.

This paper is available as a pdf (428kB) file. It is also on the arXiv: arxiv.org/abs/1807.07457.

 Saturday, July 21, 2018