Ordered set partitions and the 0-Hecke algebra

Jia Huang; Brendon Rhoades

Ordered set partitions and the 0-Hecke algebra

Jia Huang, Brendon Rhoades

Mathematics and Statistics

Research output: Contribution to conference › Paper › peer-review

5 Scopus citations

Abstract

Haglund, Rhoades, and Shimozono recently introduced a quotient R_n_,k of the polynomial ring Q[x₁,..., 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)
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
Country/Territory	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

Cite this

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title = "Ordered set partitions and the 0-Hecke algebra",

abstract = "Haglund, Rhoades, and Shimozono recently introduced a quotient Rn,k of the polynomial ring Q[x1,..., xn] depending on two positive integers k = n, which reduces to the classical coinvariant algebra of the symmetric group Sn if k = n. They determined the graded Sn-module structure of Rn,k and related it to the Delta Conjecture in the theory of Macdonald polynomials. We introduce an analogous quotient Sn,k and determine its structure as a graded module over the (type A) 0-Hecke algebra Hn(0), a deformation of the group algebra of Sn. When k = n we recover earlier results of the first author regarding the Hn(0)-action on the coinvariant algebra.",

keywords = "Coinvariant algebra, Hecke algebra, Set partition",

author = "Jia Huang and Brendon Rhoades",

note = "Funding Information: ∗[email protected] †[email protected]. Brendon Rhoades was partially supported by NSF Grant DMS-1500838. Publisher Copyright: {\textcopyright} FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018 ; Conference date: 16-07-2018 Through 20-07-2018",

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T1 - Ordered set partitions and the 0-Hecke algebra

AU - Huang, Jia

AU - Rhoades, Brendon

N1 - Funding Information: ∗[email protected] †[email protected]. Brendon Rhoades was partially supported by NSF Grant DMS-1500838. Publisher Copyright: © FPSAC 2018 - 30th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

PY - 2018

Y1 - 2018

N2 - Haglund, Rhoades, and Shimozono recently introduced a quotient Rn,k of the polynomial ring Q[x1,..., xn] depending on two positive integers k = n, which reduces to the classical coinvariant algebra of the symmetric group Sn if k = n. They determined the graded Sn-module structure of Rn,k and related it to the Delta Conjecture in the theory of Macdonald polynomials. We introduce an analogous quotient Sn,k and determine its structure as a graded module over the (type A) 0-Hecke algebra Hn(0), a deformation of the group algebra of Sn. When k = n we recover earlier results of the first author regarding the Hn(0)-action on the coinvariant algebra.

AB - Haglund, Rhoades, and Shimozono recently introduced a quotient Rn,k of the polynomial ring Q[x1,..., xn] depending on two positive integers k = n, which reduces to the classical coinvariant algebra of the symmetric group Sn if k = n. They determined the graded Sn-module structure of Rn,k and related it to the Delta Conjecture in the theory of Macdonald polynomials. We introduce an analogous quotient Sn,k and determine its structure as a graded module over the (type A) 0-Hecke algebra Hn(0), a deformation of the group algebra of Sn. When k = n we recover earlier results of the first author regarding the Hn(0)-action on the coinvariant algebra.

KW - Coinvariant algebra

KW - Hecke algebra

KW - Set partition

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M3 - Paper

AN - SCOPUS:85042744014

T2 - 30th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2018

Y2 - 16 July 2018 through 20 July 2018

ER -

Ordered set partitions and the 0-Hecke algebra

Abstract

Conference

Keywords

ASJC Scopus subject areas

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