2013/11/02 by Rafael Stekolshchik, Stekolshchik, Rafael
Chemistry · Mathematics · #06B15 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Representation Theory (math.RT) #math.RT #msc:06B15
paper · pdf · doi:10.48550/arxiv.1311.0377
64 pages, 11 figures. This talk was presented at Workshop "Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities", 2008 (Banff, Canada)
arxiv created 2013/11/02 · openalex publication_date 2013/11/02 · arxiv updated 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This talk was presented at Workshop "Spectral Methods in Representation Theory of Algebras and Applications to the Study of Rings of Singularities", 2008 (Banff, Canada). W. Ebeling established a connection between certain Poincare series, the Coxeter transformation C, and the corresponding affine Coxeter transformation Ca (in the context of the McKay correspondence). We consider the generalized Poincare series [PG(t)]0 for the case of multiply-laced diagrams(in the context of the McKay-Slodowy correspondence) and extend the Ebeling theorem for this case: [PG(t)]0 = X(t2)/X(t2), where X is the characteristic polynomial of the Coxeter transformation and X is the characteristic polynomial of the corresponding affine Coxeter transformation. We obtain that Poincare series coincide for pairs of diagrams obtained by folding: X (Γ) / X (Γ) = X (Γf) / X (Γf), where Γ is any (A, D, E type) Dynkin diagram, Γ is the extended Dynkin diagram, and the diagrams Γf and Γf are obtained by folding from Γ and Γ, respectively.