The coinvariant algebra is a well-studied -module that is a graded version of the regular representation of . Using a straightening algorithm on monomials and the Garsia–Stanton basis, Adin, Brenti, and Roichman gave a description of the Frobenius image of , graded by partitions, in terms of descents of standard Young tableaux. Motivated by the Delta Conjecture of Macdonald polynomials, Haglund, Rhoades, and Shimozono gave an extension of the coinvariant algebra and an extension of the Garsia–Stanton basis. Chan and Rhoades further extend these results from to the complex reflection group by defining a module that generalizes the coinvariant algebra for . We extend the results of Adin, Brenti, and Roichman to and and connect the results for to skew ribbon tableaux and a crystal structure defined by Benkart et al.
Revised: 2020-01-13
Accepted: 2020-01-13
Published online: 2020-08-20
Classification: 05E10, 05E05, 20C30, 05E15
Keywords: Young tableaux, representation theory, descent monomials.
@article{ALCO_2020__3_4_805_0, author = {Meyer, Kyle P.}, title = {Descent representations for generalized coinvariant algebras}, journal = {Algebraic Combinatorics}, pages = {805--830}, publisher = {MathOA foundation}, volume = {3}, number = {4}, year = {2020}, doi = {10.5802/alco.109}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2020__3_4_805_0/} }
Meyer, Kyle P. Descent representations for generalized coinvariant algebras. Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 805-830. doi : 10.5802/alco.109. https://alco.centre-mersenne.org/item/ALCO_2020__3_4_805_0/
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