Imaginary Verma modules and Kashiwara algebras for $U_q(\widehat{\mathfrak{sl}(2)})$

Cox, Ben; Futorny, Vyacheslav; Misra, Kailash C.

Imaginary Verma modules and Kashiwara algebras for $U_q(\widehat{\mathfrak{sl}(2)})$

Authors

Cox, Ben

Futorny, Vyacheslav

Misra, Kailash C.

Description

We consider imaginary Verma modules for quantum affine algebra $U_q(\hat{\mathfrak{sl}(2)})$ and construct Kashiwara type operators and the Kashiwara algebra $\mathcal K_q$. We show that a certain quotient $\mathcal N_q^-$ of $U_q(\hat{\mathfrak{sl}(2)})$ is a simple $\mathcal K_q$-module.