Quasimodular forms and sl(m|m)^ characters

TL;DR

This paper explores the automorphic properties and asymptotic behaviors of characters related to affine superalgebra modules, specifically focusing on the case where m equals n, extending previous work on related algebraic structures.

Contribution

It introduces new automorphic and asymptotic analyses for characters of s ext{l}(m|m)^ ext{wedge} modules, extending prior results from the case m>n to m=n.

Findings

Automorphic properties of characters established for m=n case.

Asymptotic behaviors of these characters analyzed.

Extension of previous work from m>n to m=n case.

Abstract

In this paper, we establish automorphic properties and asymptotic behaviors of characters due to Kac-Wakimoto pertaining to $s\ell(m|n)^\wedge$ highest weight modules in the case $m=n$, extending work of the first author and Ono \cite{BOKac} and the first two authors \cite{BF} which pertains to the case $m>n$.