## Abstract

Haglund, Rhoades, and Shimozono recently introduced a quotient R_{n}_{,k} of the polynomial ring Q[x_{1},..., x_{n}] depending on two positive integers k = n, which reduces to the classical coinvariant algebra of the symmetric group S_{n} if k = n. They determined the graded S_{n}-module structure of R_{n}_{,k} and related it to the Delta Conjecture in the theory of Macdonald polynomials. We introduce an analogous quotient S_{n}_{,k} and determine its structure as a graded module over the (type A) 0-Hecke algebra H_{n}(0), a deformation of the group algebra of S_{n}. When k = n we recover earlier results of the first author regarding the H_{n}(0)-action on the coinvariant algebra.

Original language | English (US) |
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State | Published - 2018 |

Event | 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 - Hanover, United States Duration: Jul 16 2018 → Jul 20 2018 |

### Conference

Conference | 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 |
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Country | United States |

City | Hanover |

Period | 7/16/18 → 7/20/18 |

## Keywords

- Coinvariant algebra
- Hecke algebra
- Set partition

## ASJC Scopus subject areas

- Algebra and Number Theory