Restricted representations of the twisted N=2 superconformal algebra

2023/03/13 by Haibo Chen, Chen, Haibo, Su, Yucai +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2303.06898

openalex publication_date 2023/03/13 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct a large class of new simple modules over the twisted N=2 superconformal algebra. These new simple modules are restricted modules based on the simple modules over certain finite-dimensional solvable Lie superalgebras, including various versions of Whittaker modules. We elaborate that they are also the twisted modules for the universal N=2 superconformal vertex algebra. On the other hand, we give an explicit characterization of the simple restricted modules over the twisted N=2 superconformal algebra T under the condition that T_t in T acts injectively for some t∈ (1)/(2)+\Z₊.

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