Admissible sl(2/1) Characters and Parafermions

TL;DR

This paper computes the branching functions of affine superalgebra sl(2/1) characters into sl(2) characters at fractional levels, involving rational torus and parafermion characters, advancing understanding of superalgebra representations.

Contribution

It introduces explicit calculations of branching functions for sl(2/1) at fractional levels, connecting superalgebra characters with rational torus and parafermion characters.

Findings

Branching functions expressed in terms of rational torus and parafermion characters.

Explicit formulas for fractional level representations of sl(2/1).

Enhanced understanding of superalgebra character decompositions.

Abstract

The branching functions of the affine superalgebra $sl(2/1)$ characters into characters of the affine subalgebra $sl(2)$ are calculated for fractional levels $k=1/u-1$, u positive integer. They involve rational torus $A_{u(u-1)}$ and $Z_{u-1}$ parafermion characters.