Hecke algebras of simply-laced type with independent parameters

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Abstract

We study the (complex) Hecke algebra HS(q) of a finite simply-laced Coxeter system (W, S) with independent parameters q ∈ (C\{roots of unity})S. We construct its irreducible representations and projective indecomposable representations. We obtain the quiver of this algebra and determine when it is of finite representation type. We provide decomposition formulas for induced and restricted representations between the algebra HS(q) and the algebra HR(q|R) with R ⊆ S. Our results demonstrate an interesting combination of the representation theory of finite Coxeter groups and their 0-Hecke algebras, including a two-sided duality between the induced and restricted representations.

Original languageEnglish (US)
Pages (from-to)667-691
Number of pages25
JournalAlgebraic Combinatorics
Volume3
Issue number3
DOIs
StatePublished - 2020

Keywords

  • Duality
  • Hecke algebra
  • Independent parameters
  • Induction and restriction
  • Simply-laced Coxeter system

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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