Generalized Weyl modules and Demazure submodules of level-zero extremal weight modules

TL;DR

This paper establishes a quantum analog relationship between generalized Weyl modules and Demazure submodules of extremal weight modules over quantum affine algebras, revealing new structural insights.

Contribution

It proves that a specific quotient of Demazure submodules is a quantum analog of generalized Weyl modules, linking two important module classes.

Findings

Demonstrated the quantum analog relationship between modules

Identified specific quotients of Demazure modules as generalized Weyl modules

Enhanced understanding of module structures over quantum affine algebras

Abstract

We study a relationship between the graded characters of generalized Weyl modules $W_{w \lambda}$, $w \in W$, over the positive part of the affine Lie algebra and those of specific quotients $V_{w}^- (\lambda) / X_{w}^- (\lambda)$, $w \in W$, of the Demazure submodules $V_{w}^- (\lambda)$ of the extremal weight modules $V(\lambda)$ over the quantum affine algebra, where $W$ is the finite Weyl group and $\lambda$ is a dominant weight. More precisely, we prove that a specific quotient of the Demazure submodule is a quantum analog of a generalized Weyl module.