Vertex Operator Superalgebras and Odd Trace Functions

2013/07/15 by Jethro van Ekeren, van Ekeren, Jethro
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1307.4114

openalex publication_date 2013/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We begin by reviewing Zhu's theorem on modular invariance of trace functions associated to a vertex operator algebra, as well as a generalisation by the author to vertex operator superalgebras. This generalisation involves objects that we call `odd trace functions'. We examine the case of the N=1 superconformal algebra. In particular we compute an odd trace function in two different ways, and thereby obtain a new representation theoretic interpretation of a well known classical identity due to Jacobi concerning the Dedekind eta function.

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