Kostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series

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dc.creatorStekolshchik, Rafael
dc.date2006-08-20
dc.date.accessioned2026-07-07T07:21:57Z
dc.date.available2026-07-07T07:21:57Z
dc.descriptionWe generalize B. Kostant's construction of generating functions to the case of multiply-laced diagrams and we prove for this case W. Ebeling's theorem which connects the Poincare series [P_G(t)]_0 and the Coxeter transformations. According to W. Ebeling's theorem [P_G(t)]_0 = \frac{X(t^2)}{\tilde{X}(t^2)}, where X is the characteristic polynomial of the Coxeter transformation and \tilde{X} is the characteristic polynomial of the corresponding affine Coxeter transformation. We prove McKay's observation relating the Poincare series [P_G(t)]_i: (t+t^{-1})[P_G(t)]_i = \sum\limits_{i \leftarrow j}[P_G(t)]_j, where j runs over all vertices adjacent to i.
dc.description22 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0608500
dc.identifierhttp://arxiv.org/abs/math/0608500
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115489
dc.subjectRepresentation Theory
dc.subject20F55, 15A18, 17B67
dc.titleKostant's generating functions, Ebeling's theorem and McKay's observation relating the Poincare series
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