The authors link suitably generalized deformed phi-coordinated modules of the quantum affine vertex algebra V^c(gl_N) to representations of U_h(gl_N) and O_h(Mat_N), showing that its center at critical level c=-N produces q-analogues of quantum immanants.
Twisted quantum affine algebras and equivariant $\phi$-coordinated modules for quantum vertex algebras
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abstract
This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\hbar$-adic versions of the smash product construction of quantum vertex algebras and their $\phi$-coordinated quasi modules, which were obtained before in a sequel, we construct a family of $\hbar$-adic quantum vertex algebras $V_L[[\hbar]]^{\eta}$ as deformations of the lattice vertex algebras $V_L$, and establish a natural connection between twisted quantum affine algebras of type $A, D, E$ and equivariant $\phi$-coordinated quasi modules for the $\hbar$-adic quantum vertex algebras $V_L[[\hbar]]^{\eta}$ with certain specialized $\eta$.
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Evaluation-type deformed modules over the quantum affine vertex algebras of type $A$
The authors link suitably generalized deformed phi-coordinated modules of the quantum affine vertex algebra V^c(gl_N) to representations of U_h(gl_N) and O_h(Mat_N), showing that its center at critical level c=-N produces q-analogues of quantum immanants.