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JUCYS–MURPHY ELEMENTS AND CENTRES OF CELLULAR ALGEBRAS

Part of: Conditions on elements

Published online by Cambridge University Press:  15 December 2011

YANBO LI
YANBO LI*
Affiliation:
Department of Information and Computing Sciences, Northeastern University at Qinhuangdao, Qinhuangdao 066004, PR China School of Mathematics Sciences, Beijing Normal University, Beijing 100875, PR China (email: [email protected])
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Abstract

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Let R be an integral domain and A a cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ and S,T∈M(λ)}. Suppose that A is equipped with a family of Jucys–Murphy elements which satisfy the separation condition in the sense of Mathas [‘Seminormal forms and Gram determinants for cellular algebras’, J. reine angew. Math.619 (2008), 141–173, with an appendix by M. Soriano]. Let K be the field of fractions of R and AK=A⨂ RK. We give a necessary and sufficient condition under which the centre of AK consists of the symmetric polynomials in Jucys–Murphy elements. We also give an application of our result to Ariki–Koike algebras.

Keywords

Jucys–Murphy elementscellular algebrascentres

MSC classification

Secondary: 16U70: Center, normalizer (invariant elements)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 2 , April 2012 , pp. 261 - 270
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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