The characteristic polynomials of imprimitive groups and affine Coxeter groups

2025/05/16 by Feng, Chenyue, Shoumin Liu, Liu, Shoumin +2
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2505.10788

openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will seek appropriate generators to define the characteristic polynomials of G(r,1,n), and prove that for every finite dimensional representation of G(r,1,n), the characteristic polynomial of G(r,1,n) determines the character of this representation. Furthermore, the same conclusion holds for affine Coxeter groups \(\widetildeW\) and G(r,p,n).

Citations

• Characteristic polynomials for classical Lie algebras
• More on characteristic polynomials of Lie algebras
• The Characteristic Polynomial of Projections
• Clifford theory on rational Cherednik algebras of imprimitive groups
• Joint spectrum and infinite dihedral group

Related

• Characteristic polynomials of the weak order on classical and affine Coxeter groups
• Characteristic polynomials and some combinatorics for finite Coxeter groups
• The generalized characteristic polynomial, corresponding resolvent and their application
• On polynomial representations of finite groups
• Projective Joint Spectra and Characters of representations of A_n