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 (6)

• Mock Theta Functions
• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Integrable highest weight modules over affine superalgebras and Appell's function
• Fusion rules for N=2 superconformal modules
• Almost harmonic Maass forms and Kac-Wakimoto characters
• Characters of (relatively) integrable modules over affine Lie superlagebras

Cited by in corpus (6)

• 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
• Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras
• H-Harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Some Indefinite Theta Series
• A characterization of modified mock theta functions