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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, February 15, 2018 - 3:00pm

Kyle Meyer

UC San Diego


University of Pennsylvania


The coinvariant algebra R_n is a well-studied S_n-module that gives a graded version of the regular representation of S_n. Motivated by the Delta Conjecture in the field of Macdonald polynomials, Haglund, Rhoades, and Shimozono define a graded algebra and S_n-module R_{n,k} that generalizes the coinvariant algebra. For the classical coinvariant algebra, Adin, Brenti, and Roichman give a refinement of the grading that is indexed by partitions and whose isomorphism types are determined by descents of standard Young tableaux. 

In this talk I will cover these algebras and give an extension of the results of Adin, Brenti, and Roichman to R_{n,k}.  Additionally I will relate this extension to the work of "Team Schilling" on a minimaj crystal and skew ribbon tableaux, and I will discuss a method for finding further generalizations using a method of Garsia and Procesi.