Geodesic
0-Hecke algebra actions on coinvariants and flags
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 245-278.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The 0-Hecke algebra $H_n(0)$ is a deformation of the group algebra of the symmetric group $\mathfrak{S}_n$. We show that its coinvariant algebra naturally carries the regular representation of $H_n(0)$, giving an analogue of the well-known result for $\mathfrak{S}_n$ by Chevalley-Shephard-Todd. By investigating the action of $H_n(0)$ on coinvariants and flag varieties, we interpret the generating functions counting the permutations with fixed inverse descent set by their inversion number and major index. We also study the action of $H_n(0)$ on the cohomology rings of the Springer fibers, and similarly interpret the (non-commutative) Hall-Littlewood symmetric functions indexed by hook shapes.
Classification : 05E15, 20C08, 20B30
Keywords: 0-Hecke algebra, coinvariant algebra, Demazure operator, descent monomial, flag variety, Hall-Littlewood function, Ribbon number, Springer fiber 
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     author = {Huang, Jia},
     title = {0-Hecke algebra actions on coinvariants and flags},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2014__40_1_a2/}
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Huang, Jia. 0-Hecke algebra actions on coinvariants and flags. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 1, pp. 245-278. http://geodesic.mathdoc.fr/item/JAC_2014__40_1_a2/