Character formulas and descents for the hyperoctahedral group

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

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

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 Désarménien and Wachs.

Original languageEnglish
Pages (from-to)128-169
Number of pages42
JournalAdvances in Applied Mathematics
Volume87
DOIs
StatePublished - 1 Jun 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

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

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