On representation theory of cyclotomic Hecke-Clifford algebras

2025/01/12 by Shi, Lei, Wan, Jinkui
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2501.06763

Abstract

In this article, we give an explicit construction of the simple modules for both non-degenerate and degenerate cyclotomic Hecke-Clifford superalgebras over an algebraically closed field of characteristic not equal to 2 under certain condition in terms of parameters in defining these algebras. As an application, we obtain a sufficient condition on the semi-simplicity of these cyclotomic Hecke-Clifford superalgebras via a dimension comparison. As a byproduct, both generic non-degenerate and degenerate cyclotomic Hecke-Clifford superalgebras are shown to be semisimple.

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