Cellularity of cyclotomic Yokonuma-Hecke algebras

2015/06/24 by Cui, Weideng
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1506.07321

Abstract

We first give a direct proof of a basis theorem for the cyclotomic Yokonuma-Hecke algebra Y_r,n^d(q). Our approach follows Kleshchev's, which does not use the representation theory of Y_r,n^d(q), and so it is very different from that of [ChP2]. We also present two applications. Then we prove that the cyclotomic Yokonuma-Hecke algebra Y_r,n^d(q) is cellular by constructing an explicit cellular basis, and show that the Jucys-Murphy elements for Y_r,n^d(q) are JM-elements in the abstract sense. In the appendix, we shall develop the fusion procedure for Y_r,n^d(q).

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