Geodesic
Type A admissible cells are Kazhdan–Lusztig
Nguyen, Van Minh1
1 School of Mathematics and Statistics University of Sydney NSW 2006, Australia
Algebraic Combinatorics, Tome 3 (2020) no. 1, pp. 55-105.

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

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DOI : 10.5802/alco.91
Classification : 05E10, 20C08
Mots-clés : 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Nguyen, Van Minh. Type $A$ admissible cells are Kazhdan–Lusztig. Algebraic Combinatorics, Tome 3 (2020) no. 1, pp. 55-105. doi : 10.5802/alco.91. https://geodesic-test.mathdoc.fr/articles/10.5802/alco.91/

[1] Assaf, Sami H. Dual equivalence graphs I: A new paradigm for Schur positivity, Forum Math. Sigma, Volume 3 (2015), e12, 33 pages | MR | Zbl

[2] Brini, Andrea Combinatorics, superalgebras, invariant theory and representation theory, Séminaire Lotharingien de Combinatoire, Volume 55 (2007), B55g, 117 pages | MR | Zbl

[3] Castronuovo, Niccoló The dominance order for permutations, Pure Math. Appl. (PU.M.A.), Volume 25 (2015) no. 1, pp. 45-62 | Zbl | MR

[4] Chmutov, Michael Type A molecules are Kazhdan–Lusztig, J. Algebr. Comb., Volume 42 (2015) no. 4, pp. 1059-1076 | DOI | MR | Zbl

[5] Deodhar, Vinay V. Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math., Volume 39 (1977) no. 2, pp. 187-198 | DOI | Zbl

[6] Elias, Ben; Williamson, Geordie The Hodge theory of Soergel bimodules, Ann. Math. (2), Volume 180 (2014) no. 3, pp. 1089-1136 | MR | Zbl | DOI

[7] Geck, Meinolf Kazhdan–Lusztig cells and the Murphy basis, Proc. Lond. Math. Soc. (3), Volume 93 (2006) no. 3, pp. 635-665 | DOI | MR | Zbl

[8] Geck, Meinolf; Pfeiffer, Götz Characters of finite Coxeter groups and Iwahori–Hecke algebras, Lond. Math. Soc. Monogr., New Ser., Oxford University Press, 2000 no. 21 | Zbl

[9] Kazhdan, David; Lusztig, George Representations of Coxeter groups and Hecke algebras, Invent. Math., Volume 53 (1979) no. 2, pp. 165-184 | DOI | Zbl | MR

[10] Mathas, Andrew Iwahori–Hecke algebras and Schur algebras of the symmetric group, Univ. Lect. Ser., 15, American Mathematical Society, 1999 | Zbl | MR

[11] Nguyen, Van Minh W-graph ideals II, J. Algebra, Volume 361 (2012) no. 2, pp. 248-263 | DOI | Zbl

[12] Sagan, Bruce E. The symmetric group: representations, combinatorial algorithms, and symmetric functions, Grad. Texts Math., 203, Springer, 2001 | Zbl

[13] Stembridge, John R. Admissible W-graphs, Represent. Theory, Volume 12 (2008) no. 14, pp. 346-368 | DOI | Zbl | MR

[14] Stembridge, John R. More W-graphs and cells: molecular components and cell synthesis (2008) (Atlas of Lie Groups AIM Workshop VI)

[15] Stembridge, John R. A finiteness theorem for W-graphs, Adv. Math., Volume 229 (2012) no. 4, pp. 2405-2414 | MR | Zbl | DOI

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