Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group

2012/05/30 by Francis, Andrew, Jones, Lenny
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1205.6837

Abstract

Let \H_n be the Iwahori-Hecke algebra of the symmetric group S_n, and let Z(\H_n) denote its centre. Let B=b₁,b₂,...,b_t be a basis for Z(\H_n) over R=\Z[q,q^-1]. Then B is called multiplicative if, for every i and j, there exists k such that b_ib_j= b_k. In this article we prove that there are no multiplicative bases for Z(\Z S_n) and Z(\H_n) when n≥ 3. In addition, we prove that there exist exactly two multiplicative bases for Z(\Z S₂) and none for Z(\H₂).

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