Center of the quantum affine vertex algebra in type A

Abstract

We consider the quantum vertex algebra associated with the double Yangian in type A as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct algebraically independent families of topological generators of the center at the critical level.

39 pages, few corrections made

References in corpus (7)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• On higher order Sugawara operators
• Manin matrices and Talalaev's formula
• Higher Sugawara operators for the quantum affine algebras of type A
• Quantization of the shift of argument subalgebras in type A
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Cited by in corpus (18)

• $h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$
• On the structure of quantum vertex algebras
• Double Yangian and the universal R-matrix
• Yangian doubles of classical types and their vertex representations
• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• di-Langlands correspondence and extended observables
• The formal shift operator on the Yangian double
• $h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\varphi$-coordinated modules
• Double Yangian and reflection algebras of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Quantum current algebras associated with rational $R$-matrix
• Quasi modules for the quantum affine vertex algebra in type $A$
• Center of the Yangian double in type A
• Principal subspaces for the quantum affine vertex algebra in type $A_1^{(1)}$
• Semi-infinite construction for the double Yangian of type $A_1^{(1)}$
• Quantum Sugawara operators in type $A$
• A note on constructing quasi modules for quantum vertex algebras from twisted Yangians
• On the $h$-adic quantum vertex algebras associated with Hecke symmetries
• On two families of quantum vertex algebras of FRT-type