On quantum vertex algebras and their modules

Abstract

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras with quantum vertex algebras.

18 pages; contribution to the proceedings of the conference in honor of Professor Geoffrey Mason

References in corpus (8)

• Field Algebras
• Constructing quantum vertex algebras
• $H_D$-Quantum Vertex Algebras and Bicharacters
• Modules-at-infinity for quantum vertex algebras
• Super-bicharacter construction of quantum vertex algebras
• Some quantum vertex algebras of Zamolodchikov-Faddeev type
• Symmetric polynomials and $H_D$-quantum vertex algebras
• $\hslash$-adic quantum vertex algebras and their modules

Cited by in corpus (19)

• Center of the quantum affine vertex algebra in type A
• $h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$
• On the structure of quantum vertex algebras
• Quantum vertex $F((t))$-algebras and their modules
• Quantum affine vertex algebras associated to untwisted quantum affinization algebras
• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• Center of the quantum affine vertex algebra associated with trigonometric R-matrix
• $h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\varphi$-coordinated modules
• Quasi modules for the quantum affine vertex algebra in type $A$
• Quantum current algebras associated with rational $R$-matrix
• Quantum vertex algebras and their phi-coordinated quasi modules
• Twisted quantum affinizations and quantization of extended affine Lie algebras
• Yangian deformations of $\mathcal{S}$-commutative quantum vertex algebras and Bethe subalgebras
• On the Heisenberg algebra associated with the rational $R$-matrix
• On the $h$-adic quantum vertex algebras associated with Hecke symmetries
• A note on constructing quasi modules for quantum vertex algebras from twisted Yangians
• On two families of quantum vertex algebras of FRT-type
• Classical and quantum conformal field theories
• Principal subspaces for the quantum affine vertex algebra in type $A_1^{(1)}$