### 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) |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*147*(5), 1839-1850. https://doi.org/10.1090/proc/14157

**Hall-littlewood polynomials and a hecke action on ordered set partitions.** / Huang, Jia; Rhoades, Brendon; Scrimshaw, Travis; Hersh, Patricia.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 147, no. 5, pp. 1839-1850. https://doi.org/10.1090/proc/14157

}

TY - JOUR

T1 - Hall-littlewood polynomials and a hecke action on ordered set partitions

AU - Huang, Jia

AU - Rhoades, Brendon

AU - Scrimshaw, Travis

AU - Hersh, Patricia

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - Coinvariant algebra

KW - Hecke algebra

KW - Ordered set partition

KW - Symmetric function

UR - http://www.scopus.com/inward/record.url?scp=85065478963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065478963&partnerID=8YFLogxK

U2 - 10.1090/proc/14157

DO - 10.1090/proc/14157

M3 - Article

AN - SCOPUS:85065478963

VL - 147

SP - 1839

EP - 1850

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -