Representations of affine superalgebras and mock theta functions III

Abstract

We study modular invariance of normalized supercharacters of tame integrable modules over an affine Lie superalgebra, associated to an arbitrary basic Lie superalgebra $\mathfrak{g}.$ For this we develop a several step modification process of multivariable mock theta functions, where at each step a Zwegers' type "modifier" is used. We show that the span of the resulting modified normalized supercharacters is $S{L}_2(\mathbb{Z})$-invariant, with the transformation matrix equal, in the case the Killing form on $\mathfrak{g}$ is non-degenerate, to that for the subalgebra ${\mathfrak{g}}^{!}$ of $\mathfrak{g},$ orthogonal to a maximal isotropic set of roots of $\mathfrak{g}.$

References in corpus (2)

• Mock Theta Functions
• Characters of (relatively) integrable modules over affine Lie superlagebras

Cited by in corpus (4)

• Tensor categories for vertex operator superalgebra extensions
• Indefinite theta series and generalized error functions
• Extension of the osp(m|n)~ so(m-n) Correspondence to the Infinite-Dimensional Chiral Spinors and Self Dual Tensors
• A characterization of modified mock theta functions