English

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

Representation Theory 2023-05-16 v3

Abstract

In this paper we obtain explicit formulas for mock theta functions Φ[m,s](τ,z1,z2,t)\Phi^{[m,s]}(\tau, z_1, z_2,t) (m12N,s12Z)(m \in \frac12 \mathbf{N}, s \in \frac12 \mathbf{Z}) by using the coroot lattice of the Lie superalgebra D(2,1,a)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.

Keywords

Cite

@article{arxiv.2209.00234,
  title  = {Mock theta functions and characters of N=3 superconformal modules IV},
  author = {Minoru Wakimoto},
  journal= {arXiv preprint arXiv:2209.00234},
  year   = {2023}
}