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

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