Principally specialized characters of sl(m|1)^-modules

TL;DR

This paper computes specialized characters of certain affine superalgebra modules, revealing their expression as infinite products and deriving quasiparticle-type formulas, advancing understanding of their structure.

Contribution

It introduces explicit formulas for principally specialized characters of level 1 $ ext{sl}(m|1)$-modules, including infinite product and quasiparticle-type character formulas.

Findings

Principally specialized characters expressed as infinite products.

Derived quasiparticle-type character formulas.

Computed characters for basic modules $L(\\Lambda_0)$.

Abstract

In this paper, we calculate a series of principally specialized characters of the $\hat{\mathfrak{sl}}(m|1)$-modules of level 1. In particular, we show that the principally specialized characters of the basic modules $L(\Lambda_0)$ is expressed as an infinite product. And we deduce the specialized character formula of ``quasiparticle'' type.