Ordered set partitions and the 0-Hecke algebra

Jia Huang, Brendon Rhoades

Research output: Contribution to conferencePaperpeer-review

5 Scopus citations

Abstract

Haglund, Rhoades, and Shimozono recently introduced a quotient Rn,k of the polynomial ring Q[x1,..., xn] depending on two positive integers k = n, which reduces to the classical coinvariant algebra of the symmetric group Sn if k = n. They determined the graded Sn-module structure of Rn,k and related it to the Delta Conjecture in the theory of Macdonald polynomials. We introduce an analogous quotient Sn,k and determine its structure as a graded module over the (type A) 0-Hecke algebra Hn(0), a deformation of the group algebra of Sn. When k = n we recover earlier results of the first author regarding the Hn(0)-action on the coinvariant algebra.

Original languageEnglish (US)
StatePublished - 2018
Event30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States
Duration: Jul 16 2018Jul 20 2018

Conference

Conference30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018
CountryUnited States
CityHanover
Period7/16/187/20/18

Keywords

  • Coinvariant algebra
  • Hecke algebra
  • Set partition

ASJC Scopus subject areas

  • Algebra and Number Theory

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