Representations of affine superalgebras and mock theta functions

2013/08/06 by Kac, Victor G., Wakimoto, Minoru
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1308.1261

Abstract

We show that the normalized supercharacters of principal admissible modules over the affine Lie superalgebra sℓ_2|1 (resp. psℓ_2|2) can be modified, using Zwegers' real analytic corrections, to form a modular (resp. S-) invariant family of functions. Applying the quantum Hamiltonian reduction, this leads to a new family of positive energy modules over the N=2 (resp. N=4) superconformal algebras with central charge 3(1-(2m+2)/(M)), where m ∈ ℤ_{≥ 0}, M∈ ℤ_{≥ 2}, gcd(2m+2,M)=1 if m>0 (resp. 6((m)/(M)-1), where m ∈ ℤ_{≥ 1}, M∈ ℤ_{≥ 2}, gcd(2m,M)=1 if m>1), whose modified characters and supercharacters form a modular invariant family.

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