  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.
