Representations of affine superalgebras and mock theta functions II

2014/02/04 by Victor G. Kač, Victor G. Kac, Minoru Wakimoto +2
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Pharmacological Receptor Mechanisms and Effects #math.RT

paper · pdf · doi:10.48550/arxiv.1402.0727

arxiv created 2014/02/04 · arxiv updated 2014/02/05

Abstract

We show that the normalized supercharacters of principal admissible modules, associated to each integrable atypical module over the affine Lie superalgebra \widehatsl_2|1 can be modified, using Zwegers' real analytic corrections, to form an SL₂(Z)-invariant family of functions. Using a variation of Zwegers' correction, we obtain a similar result for \widehatosp_3|2. Applying the quantum Hamiltonian reduction, this leads to new families of positive energy modules over the N=2 (resp. N=3) superconformal algebras with central charge c=3 (1-(2m+2)/(M)), where m ∈ Z_{≥ 0}, M ∈ Z_{≥ 2}, gcd(2m+2,M)=1 if m>0 (resp. c=-3(2m+1)/(M), where m ∈ Z_{≥ 0}, M ∈ Z_{≥ 2} gcd(4m +2, M) =1), whose modified supercharacters form an SL₂(Z)-invariant family of functions.

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