Modules-at-infinity for quantum vertex algebras
Haisheng Li

TL;DR
This paper constructs quantum vertex algebras from double Yangians related to sl2, establishing their modules and introducing modules-at-infinity, thereby linking these structures to pseudo-differential operators on the circle.
Contribution
It introduces modules-at-infinity for quantum vertex algebras derived from double Yangians, expanding the understanding of their module theory and connections to pseudo-differential operators.
Findings
Constructed quantum vertex algebras $V_q$ from double Yangians.
Established that $DY_q(sl_2)$-modules are $V_q$-modules.
Linked modules-at-infinity to the Lie algebra of pseudo-differential operators.
Abstract
This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian , denoted by and with a nonzero complex number. For each nonzero complex number , we construct a quantum vertex algebra and prove that every -module is naturally a -module. We also show that -modules are what we call -modules-at-infinity. To achieve this goal, we study what we call -local subsets and quasi-local subsets of for any vector space , and we prove that any -local subset generates a (weak) quantum vertex algebra and that any quasi-local subset generates a vertex algebra with…
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