Mock theta functions and characters of N=3 superconformal modules IV

Minoru Wakimoto

paper

Mock theta functions and characters of N=3 superconformal modules IV

arXiv:2209.00234

Abstract

In this paper we obtain explicit formulas for mock theta functions $Φ^{[m, s]} (τ, z_{1}, z_{2}, t)$ $(m \in \frac{1}{2} N, s \in \frac{1}{2} Z)$ by using the coroot lattice of the Lie superalgebra $D (2, 1, a)$ and the Kac-Peterson's identity. As its application, we study the branching functions of tensor products of N=3 modules and prove the formula conjectured in the previous paper.