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arXiv · 2501.06763

On representation theory of cyclotomic Hecke-Clifford algebras

Lei Shi·Jinkui Wan
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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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Lei Shi, Jinkui Wan. 2025-01-12. On representation theory of cyclotomic Hecke-Clifford algebras. https://arxiv.org/abs/2501.06763

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