# Weyl modules for queer Lie superalgebras

## TL;DR

This paper introduces global and local Weyl modules for queer Lie superalgebras tensorized with a commutative algebra, establishing their universality, finite dimensionality under certain conditions, and a tensor product property.

## Contribution

It defines and analyzes Weyl modules for queer Lie superalgebras, proving their universality, finite dimensionality, and tensor product behavior under specific assumptions.

## Key findings

- Global Weyl modules are universal highest weight objects.
- Local Weyl modules are finite dimensional under certain conditions.
- Tensor product property holds for local Weyl modules.

## Abstract

We define global and local Weyl modules for $q \otimes A$, where $q$ is the queer Lie superalgebra and $A$ is an associative commutative unital $\mathbb{C}-$algebra. We prove that global Weyl modules are universal highest weight objects in certain category upto parity reversing functor $\Pi$. Then with the assumption that $A$ is finitely generated and with a special technical condition which simple root system of $q$ satisfy it is shown that the local Weyl modules are finite dimensional. Further they are universal highest map-weight objects in certain category upto $\Pi$. Finally we prove a tensor product property for local Weyl modules.