Characteristic and Coxeter polynomials for affine Lie algebras

2014/09/13 by Pantelis A. Damianou, Damianou, Pantelis A., Charalampos A. Evripidou +1
Mathematics · #06B15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:06B15

paper · pdf · doi:10.48550/arxiv.1409.3956

27 pages

arxiv created 2014/09/13 · openalex publication_date 2014/09/13 · arxiv updated 2014/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the characteristic polynomials of affine Cartan, adjacency matrices and Coxeter polynomials of the associated Coxeter system using Chebyshev polynomials. We give explicit factorization of these polynomials as products of cyclotomic polynomials. Finally, we present several different methods of obtaining the exponents and Coxeter number for affine Lie algebras. In particular we compute the exponents and Coxeter number for each conjugacy class in the case of A_n⁽¹⁾.

Related

• On the characteristic polynomial of Cartan matrices and Chebyshev polynomials
• More on characteristic polynomials of Lie algebras
• Characteristic polynomials of the weak order on classical and affine Coxeter groups
• The characteristic polynomials of imprimitive groups and affine Coxeter groups
• Characteristic polynomials for classical Lie algebras