Monomial bases for the centres of the group algebra and Iwahori--Hecke algebra of S_4

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dc.creatorFrancis, Andrew
dc.creatorJones, Lenny
dc.date2007-09-04
dc.date2007-11-07
dc.date.accessioned2026-07-07T08:40:55Z
dc.date.available2026-07-07T08:40:55Z
dc.descriptionG. E. Murphy showed in 1983 that the centre of every symmetric group algebra has an integral basis consisting of a specific set of monomial symmetric polynomials in the Jucys--Murphy elements. While we have shown in earlier work that the centre of the group algebra of S_3 has exactly three additional such bases, we show in this paper that the centre of the group algebra of S_4 has infinitely many bases consisting of monomial symmetric polynomials in Jucys--Murphy elements, which we characterize completely. The proof of this result involves establishing closed forms for coefficients of class sums in the monomial symmetric polynomials in Jucys--Murphy elements, and solving several resulting exponential Diophantine equations with the aid of a computer. Our initial motivation was in finding integral bases for the centre of the Iwahori--Hecke algebra, and we address this question also, by finding several integral bases of monomial symmetric polynomials in Jucys--Murphy elements for the centre of the Iwahori--Hecke algebra of S_4.
dc.description21 pages. Version two contains corrections to some typos. In particular, one of the bases listed in Theorem 3.5 was wrong
dc.identifierhttps://arxiv.org/abs/0709.0326
dc.identifierhttp://arxiv.org/abs/0709.0326
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141515
dc.subjectGroup Theory
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.subject20C08
dc.titleMonomial bases for the centres of the group algebra and Iwahori--Hecke algebra of S_4
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