Weyl modules for Equivariant map Lie superalgebras

TL;DR

This paper introduces Weyl functors for equivariant map Lie superalgebras, establishing their universality and finite generation under specific conditions, thus advancing the understanding of modules over these algebraic structures.

Contribution

It defines global Weyl modules for equivariant map Lie superalgebras and proves their universality and finite generation under certain assumptions.

Findings

Global Weyl modules are universal highest weight objects.

Under finiteness conditions on A, global Weyl modules are finitely generated.

The paper extends the theory of Weyl modules to Lie superalgebras with equivariance.

Abstract

We define Weyl functors, global modules for equivariant map Lie superalgebras $(\g \otimes A)^{\Gamma}$, where $\g$ is basic classical $\mathbb{C}$- Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}$-algebra. Under certain condition on the triangular decomposition of $\g$ we prove that global Weyl modules are universal highest weight objects in certain category. Then with the assumption that $A$ is finitely generated, it is shown that the global Weyl modules are finitely generated.