Properties of some character tables related to the symmetric groups

dc.creatorBessenrodt, Christine
dc.creatorOlsson, Jorn B.
dc.creatorStanley, Richard P.
dc.date2004-03-05
dc.date.accessioned2026-07-07T05:06:08Z
dc.date.available2026-07-07T05:06:08Z
dc.descriptionWe determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups S_n and their double covers. In particular, we give a simple computation, based on the theory of Hall-Littlewood symmetric functions, of the determinant of the regular character table of S_n with respect to an integer r>1. This result had earlier been proved by Olsson in a longer and more indirect manner. As a consequence, we obtain a new proof of the Mathas' Conjecture on the determinant of the Cartan matrix of the Iwahori-Hecke algebra. When r is prime we determine the Smith normal form of the regular character table. Taking r large yields the Smith normal form of the full character table of S_n. Analogous results are then given for spin characters.
dc.identifierhttps://arxiv.org/abs/math/0403110
dc.identifierhttp://arxiv.org/abs/math/0403110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70371
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject05E10; 20C30
dc.titleProperties of some character tables related to the symmetric groups
dc.typetext

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