Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{M|N}$, II: Quantum currents
Year: 2026
Type: preprint
Abstract: In this paper, we continue our research on the double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{M|N}$. Extending the Etingof-Kazhdan construction, we introduce the structure of $h$-adic quantum vertex superalgebra on the vacuum module $V^c(\mathfrak{gl}_{M|N})$ over the double Yangian of level $c\in\mathbb{C}$. Next, we construct families of central elements in the completed double Yangian for $\mathfrak{gl}_{M|N}$ at the critical level. Finally, we show that the level $c$ restricted modules over the reflection algebra of $\mathfrak{gl}_{M|N}$ are naturally equipped with the structure of quasi $V^{2c}(\mathfrak{gl}_{M|N})$-module. By using this structure, we find explicit formulas for families of central elements in the completed reflection algebra of $\mathfrak{gl}_{M|N}$ at the critical level.
Source: arXiv (Cornell University)
Authors: Bagnoli, Lucia, Kožić, Slaven
Institutions: University of Zagreb, Sapienza University of Rome
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202349129