### Abstract

We construct an action of the Hecke algebra Hn(q) on a quotient of the polynomial ring F[x1, . . ., xn], where F = Q(q). The dimension of our quotient ring is the number of k-block ordered set partitions of {1, 2, . . ., n}. This gives a quantum analog of a construction of Haglund-Rhoades-Shimozono and interpolates between their result at q = 1 and work of Huang-Rhoades at q = 0.

Original language | English (US) |
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Pages (from-to) | 1839-1850 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 5 |

DOIs | |

State | Published - May 2019 |

### Keywords

- Coinvariant algebra
- Hecke algebra
- Ordered set partition
- Symmetric function

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Huang, J., Rhoades, B., Scrimshaw, T., & Hersh, P. (2019). Hall-littlewood polynomials and a hecke action on ordered set partitions.

*Proceedings of the American Mathematical Society*,*147*(5), 1839-1850. https://doi.org/10.1090/proc/14157