Local Weyl modules and fusion products for the current superalgebra $\mathfrak{sl}(1|2)[t]$

TL;DR

This paper investigates a class of modules for the current superalgebra sl(1|2)[t], demonstrating their realization as fusion products of generalized Kac modules, and confirming a conjecture about fusion parameter independence.

Contribution

It introduces and analyzes Chari-Venkatesh modules for sl(1|2)[t], proving their realization as fusion products and confirming a key conjecture about fusion parameters.

Findings

Chari-Venkatesh modules can be realized as fusion products of generalized Kac modules.

Fusion products are independent of fusion parameters for these modules.

Provides bases, dimension, and character formulas for Chari-Venkatesh modules.

Abstract

We study a class of modules, called Chari-Venkatesh modules, for the current superalgebra $\mathfrak{sl}(1|2)[t]$. This class contains other important modules, such as graded local Weyl, truncated local Weyl and Demazure-type modules. We prove that Chari-Venkatesh modules can be realized as fusion products of generalized Kac modules. In particular, this proves Feigin and Loktev's conjecture, that fusion products are independent of their fusion parameters in the case where the fusion factors are generalized Kac modules. As an application of our results, we obtain bases, dimension and character formulas for Chari-Venkatesh modules.