0-Hecke algebra actions on coinvariants and flags

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Abstract

The 0-Hecke algebra H n (0) is a deformation of the group algebra of the symmetric group Sn. We show that its coinvariant algebra naturally carries the regular representation of H n (0), giving an analogue of the well-known result for Sn by Chevalley-Shephard-Todd. By investigating the action of H n (0) on coinvariants and flag varieties, we interpret the generating functions counting the permutations with fixed inverse descent set by their inversion number and major index. We also study the action of H n (0) on the cohomology rings of the Springer fibers, and similarly interpret the (non-commutative) Hall-Littlewood symmetric functions indexed by hook shapes.

Original languageEnglish (US)
Pages (from-to)245-278
Number of pages34
JournalJournal of Algebraic Combinatorics
Volume40
Issue number1
DOIs
Publication statusPublished - Aug 2014

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Keywords

  • 0-Hecke algebra
  • Coinvariant algebra
  • Demazure operator
  • Descent monomial
  • Flag variety
  • Hall-Littlewood function
  • Ribbon number
  • Springer fiber

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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