Admissible $W\phantom{\rule{-0.166667em}{0ex}}$-graphs were defined and combinatorially characterized by Stembridge in []. The theory of admissible $W\phantom{\rule{-0.166667em}{0ex}}$-graphs was motivated by the need to construct $W\phantom{\rule{-0.166667em}{0ex}}$-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 $W\phantom{\rule{-0.166667em}{0ex}}$-cells are Kazhdan–Lusztig as conjectured by Stembridge in his original paper.

Revised:

Accepted:

Published online:

DOI: 10.5802/alco.91

Keywords: Coxeter groups, Hecke algebras, $W$-graphs, Kazhdan–Lusztig polynomials, cells

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@article{ALCO_2020__3_1_55_0, author = {Nguyen, Van Minh}, title = {Type $A$ admissible cells are {Kazhdan{\textendash}Lusztig}}, journal = {Algebraic Combinatorics}, pages = {55--105}, publisher = {MathOA foundation}, volume = {3}, number = {1}, year = {2020}, doi = {10.5802/alco.91}, zbl = {07169933}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.91/} }

Nguyen, Van Minh. Type $A$ admissible cells are Kazhdan–Lusztig. Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 55-105. doi : 10.5802/alco.91. http://www.numdam.org/articles/10.5802/alco.91/

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