On the Structure of a quotient of the global Weyl module for the map superalgebra $\mathfrak{sl}(2,1)$

TL;DR

This paper explicitly describes the structure and basis of certain quotients of global Weyl modules for the map superalgebra sl(2,1), extending previous results from sl_2 to superalgebras.

Contribution

It provides an explicit description and basis for quotients of global Weyl modules for sl(2,1), extending known results to superalgebras and paving the way for further generalizations.

Findings

Explicit structure of quotients of global Weyl modules for sl(2,1)

A basis for these modules is constructed

Extension of Feigin-Loktev theorem to superalgebras

Abstract

Let $A$ be a commutative, associative algebra with unity over $\mathbb{C}$. Using the definition of global Weyl modules for the map superalgebras given by Calixto, Lemay, and Savage we explicitly describe the structure of certain quotients of the global Weyl modules for the map superalgebra $\mathfrak{sl}(2,1)\otimes A$. We also give a nice basis for these modules. This work is an extension of a Theorem of Feigin and Loktev describing the structure of the Weyl module for the map algebra $\mathfrak{sl}_2\otimes A$. This work can naturally be extended to similar quotients of the global Weyl modules for $\mathfrak{sl}(n,m)\otimes A$.