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

Jia Huang; Brendon Rhoades; Travis Scrimshaw; Patricia Hersh

doi:10.1090/proc/14157

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

Jia Huang, Brendon Rhoades, Travis Scrimshaw, Patricia Hersh

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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	https://doi.org/10.1090/proc/14157
State	Published - May 2019

Keywords

Coinvariant algebra
Hecke algebra
Ordered set partition
Symmetric function

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/proc/14157

Cite this

@article{214af2b563a74b0192d2fe9df46e9567,

title = "Hall-littlewood polynomials and a hecke action on ordered set partitions",

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.",

keywords = "Coinvariant algebra, Hecke algebra, Ordered set partition, Symmetric function",

author = "Jia Huang and Brendon Rhoades and Travis Scrimshaw and Patricia Hersh",

note = "Funding Information: Received by the editors October 17, 2017, and, in revised form, March 12, 2018. 2010 Mathematics Subject Classification. Primary 05E05, 05E10. Key words and phrases. Ordered set partition, coinvariant algebra, symmetric function, Hecke algebra. The second author was partially supported by NSF Grant DMS-1500838. The third author was partially supported by NSF Grant DMS-1148634. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",

year = "2019",

month = may,

doi = "10.1090/proc/14157",

language = "English (US)",

volume = "147",

pages = "1839--1850",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "5",

}

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

N1 - Funding Information: Received by the editors October 17, 2017, and, in revised form, March 12, 2018. 2010 Mathematics Subject Classification. Primary 05E05, 05E10. Key words and phrases. Ordered set partition, coinvariant algebra, symmetric function, Hecke algebra. The second author was partially supported by NSF Grant DMS-1500838. The third author was partially supported by NSF Grant DMS-1148634. Publisher Copyright: © 2019 American Mathematical Society.

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

SN - 0002-9939

VL - 147

SP - 1839

EP - 1850

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this