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

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.

17 pages. arXiv admin note: text overlap with arXiv:1606.01067, arXiv:1511.07005