$H_D$-Quantum Vertex Algebras and Bicharacters

Abstract

We define a new class of quantum vertex algebras, based on the Hopf algebra $H_D=\mathbb{C}[D]$ of "infinitesimal translations" generated by $D$. Besides the braiding map describing the obstruction to commutativity of products of vertex operators, $H_D$-quantum vertex algebras have as main new ingredient a "translation map" that describes the obstruction of vertex operators to satisfying translation covariance. The translation map also appears as obstruction to the state-field correspondence being a homomorphism. We use a bicharacter construction of Borcherds to construct a large class of $H_D$-quantum vertex algebras. One particular example of this construction yields a quantum vertex algebra that contains the quantum vertex operators introduced by Jing in the theory of Hall-Littlewood polynomials.

46 pages

References in corpus (2)

• Constructing quantum vertex algebras
• Towards Deformed Chiral Algebras

Cited by in corpus (11)

• On quantum vertex algebras and their modules
• Principal subspaces for quantum affine algebra $U_q(A_n^{(1)})$
• Quantum vertex $F((t))$-algebras and their modules
• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$
• A note on the zeroth products of Frenkel-Jing operators
• Quantum vertex algebras and their phi-coordinated quasi modules
• Some quantum vertex algebras of Zamolodchikov-Faddeev type
• $\hslash$-adic quantum vertex algebras and their modules
• Classical and quantum conformal field theories
• Twisted tensor products of nonlocal vertex algebras
• Quantum vertex $C((t))$-algebras and quantum affine algebras