Hecke-Clifford algebras at roots of unity and conformal embeddings

2025/04/09 by Edie-Michell, Cain, Wenzl, Hans
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2504.07201

Abstract

In this paper we give a combinatorial description of the Cauchy completion of the categories E_q and SE_N recently introduced by the first author and Snyder. This in turns gives a combinatorial description of the categories Rep(U_q(\mathfraksl_N))_A where A is the ètale algebra object corresponding to the conformal embedding \mathfraksl_N level N into \mathfrakso_N²-1 level 1. In particular we give a classification of the simple objects of these categories, a formula for their quantum dimensions, and fusion rules for tensoring with the defining object. Our method of obtaining these results is the Schur-Weyl approach of studying the representation theory of certain endomorphism algebras in E_q and SE_N, which are known to be subalgebras of Hecke-Clifford algebras. We build on existing literature to study the representation theory of the Hecke-Clifford algebras at roots of unity.

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