ALGEBRAIC COMBINATORICS

no. 4

Descent representations for generalized coinvariant algebras
Algebraic Combinatorics, Volume 3 (2020) no. 4, pp. 805-830.

The coinvariant algebraĀ R n is a well-studied š¯”– n -module that is a graded version of the regular representation of š¯”– n . Using a straightening algorithm on monomials and the Garsiaā€“Stanton basis, Adin, Brenti, and Roichman gave a description of the Frobenius image ofĀ R n , 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 R n,k and an extension of the Garsiaā€“Stanton basis. Chan and Rhoades further extend these results from š¯”– n to the complex reflection group G(r,1,n) by defining a G(r,1,n) module S n,k that generalizes the coinvariant algebra for G(r,1,n). We extend the results of Adin, Brenti, and Roichman to R n,k and S n,k and connect the results for R n,k to skew ribbon tableaux and a crystal structure defined by Benkart et al.

Received: 2018-02-08
Revised: 2020-01-13
Accepted: 2020-01-13
Published online: 2020-08-20
DOI: https://doi.org/10.5802/alco.109
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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