Kashiwara Algebras and Imaginary Verma Modules for $U_q(\hat{\mathfrak{g}})$

Abstract

We consider imaginary Verma modules for quantum affine algebra $U_q(\hat{\mathfrak{g}})$, where $\hat{\mathfrak{g}}$ is of type 1 i.e. of non-twisted type, and construct Kashiwara type operators and the Kashiwara algebra ${\mathcal{K}}_q$. We show that a certain quotient ${\mathcal{N}}_q^{-}$ of $U_q(\hat{\mathfrak{g}})$ is a simple ${\mathcal{K}}_q$-module.

arXiv admin note: substantial text overlap with arXiv:1307.2941

References in corpus (1)

• An imaginary PBW basis for quantum affine algebras of type 1