Properties of the Solomon homomorphism

2003/02/25 by Christophe Hohlweg, Hohlweg, Christophe
Computer Science · Mathematics · #05E15 #20C33 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:05E15 #msc:20C33 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0302309

33 pages

arxiv created 2003/02/25 · openalex publication_date 2003/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a finite Coxeter group. In this paper, we show that the properties of the Solomon algebra homomorphism Phi (from the Solomom descent algebra to the algebra of class functions) are strongly related to enumerative results: certain joint statistics on W may be enumerated by the scalar products of appropriate characters.

Related

• Around Solomon's descent algebras
• Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four
• Generating series formulas for the structure constants of Solomon's descent algebra
• An Inductive Approach to Coxeter Arrangements and Solomon's Descent\n Algebra
• Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight