Character formulas and descents for the hyperoctahedral group

Ron M. Adin; Christos A. Athanasiadis; Sergi Elizalde; Yuval Roichman

doi:10.1016/j.aam.2017.01.004

Character formulas and descents for the hyperoctahedral group

Ron M. Adin, Christos A. Athanasiadis, Sergi Elizalde, Yuval Roichman

Department of Mathematics

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

15 Scopus citations

Abstract

A general setting to study a certain type of formulas, expressing characters of the symmetric group S_n explicitly in terms of descent sets of combinatorial objects, has been developed by two of the authors. This theory is further investigated in this paper and extended to the hyperoctahedral group B_n. Key ingredients are a new formula for the irreducible characters of B_n, the signed quasisymmetric functions introduced by Poirier, and a new family of matrices of Walsh–Hadamard type. Applications include formulas for natural B_n-actions on coinvariant and exterior algebras and on the top homology of a certain poset in terms of the combinatorics of various classes of signed permutations, as well as a B_n-analogue of an equidistribution theorem of Désarménien and Wachs.

Original language	English
Pages (from-to)	128-169
Number of pages	42
Journal	Advances in Applied Mathematics
Volume	87
DOIs	https://doi.org/10.1016/j.aam.2017.01.004
State	Published - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Funding

S.E. was partially supported by Simons Foundation grant #280575 and NSA grant H98230-14-1-0125.

Funders	Funder number
Simons Foundation	280575
National Security Agency	H98230-14-1-0125

Keywords

Character
Derangement
Descent set
Hyperoctahedral group
Quasisymmetric function
Schur-positivity
Symmetric group

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10.1016/j.aam.2017.01.004

Cite this

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abstract = "A general setting to study a certain type of formulas, expressing characters of the symmetric group Sn explicitly in terms of descent sets of combinatorial objects, has been developed by two of the authors. This theory is further investigated in this paper and extended to the hyperoctahedral group Bn. Key ingredients are a new formula for the irreducible characters of Bn, the signed quasisymmetric functions introduced by Poirier, and a new family of matrices of Walsh–Hadamard type. Applications include formulas for natural Bn-actions on coinvariant and exterior algebras and on the top homology of a certain poset in terms of the combinatorics of various classes of signed permutations, as well as a Bn-analogue of an equidistribution theorem of D{\'e}sarm{\'e}nien and Wachs.",

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AU - Athanasiadis, Christos A.

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KW - Derangement

KW - Descent set

KW - Hyperoctahedral group

KW - Quasisymmetric function

KW - Schur-positivity

KW - Symmetric group

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Character formulas and descents for the hyperoctahedral group

Abstract

Bibliographical note

Funding

Keywords

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