Affine cellularity of affine Yokonuma-Hecke algebras

2015/10/09 by Cui, Weideng
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1510.02647

Abstract

We establish an explicit algebra isomorphism between the affine Yokonuma-Hecke algebra \widehatY_r,n(q) and a direct sum of matrix algebras with coefficients in tensor products of affine Hecke algebras of type A. As an application of this result, we show that \widehatY_r,n(q) is affine cellular in the sense of Koenig and Xi, and further prove that it has finite global dimension when the parameter q is not a root of the Poincaré polynomial. As another application, we also recover the modular representation theory of \widehatY_r,n(q) previously obtained in [CW].

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