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

Jia Huang, Brendon Rhoades, Travis Scrimshaw, Patricia Hersh

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1839-1850
Number of pages12
JournalProceedings of the American Mathematical Society
Volume147
Issue number5
DOIs
StatePublished - May 2019

Fingerprint

Set Partition
Quotient ring
Hecke Algebra
Ordered Set
Polynomial ring
Algebra
Quotient
Interpolate
Polynomials
Analogue
Polynomial

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 147, No. 5, 05.2019, p. 1839-1850.

Research output: Contribution to journalArticle

Huang, Jia ; Rhoades, Brendon ; Scrimshaw, Travis ; Hersh, Patricia. / Hall-littlewood polynomials and a hecke action on ordered set partitions. In: Proceedings of the American Mathematical Society. 2019 ; Vol. 147, No. 5. pp. 1839-1850.
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