ALGEBRAIC COMBINATORICS

Type $A$ admissible cells are Kazhdan–Lusztig
Algebraic Combinatorics, Volume 3 (2020) no. 1, pp. 55-105.

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
Classification: 05E10,  20C08
Keywords: Coxeter groups, Hecke algebras, $W$-graphs, Kazhdan–Lusztig polynomials, cells
Nguyen, Van Minh 1

1 School of Mathematics and Statistics University of Sydney NSW 2006, Australia
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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. https://alco.centre-mersenne.org/articles/10.5802/alco.91/

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