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

Admissible W-graphs were defined and combinatorially characterized by Stembridge in [13]. 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.

Received : 2018-07-19
Revised : 2019-06-06
Accepted : 2019-07-21
Published online : 2020-02-12
DOI : https://doi.org/10.5802/alco.91
Classification:  05E10,  20C08
Keywords: Coxeter groups, Hecke algebras, W-graphs, Kazhdan–Lusztig polynomials, cells
@article{ALCO_2020__3_1_55_0,
     author = {Nguyen, Van Minh},
     title = {Type $A$ admissible cells are Kazhdan--Lusztig},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {3},
     number = {1},
     year = {2020},
     pages = {55-105},
     doi = {10.5802/alco.91},
     language = {en},
     url={alco.centre-mersenne.org/item/ALCO_2020__3_1_55_0/}
}
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/item/ALCO_2020__3_1_55_0/

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