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Double Yangian and reflection algebras of the Lie superalgebra glM|N, II: Quantum currents
Abstract
In this paper, we continue our research on the double Yangian and reflection algebras of the Lie superalgebra glM|N. Extending the Etingof-Kazhdan construction, we introduce the structure of h-adic quantum vertex superalgebra on the vacuum module Vc(glM|N) over the double Yangian of level c∈ℂ. Next, we construct families of central elements in the completed double Yangian for glM|N at the critical level. Finally, we show that the level c restricted modules over the reflection algebra of glM|N are naturally equipped with the structure of quasi V2c(glM|N)-module. By using this structure, we find explicit formulas for families of central elements in the completed reflection algebra of glM|N at the critical level.
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BibTeX
@misc{bagnoli2026double,
title = {{Double Yangian and reflection algebras of the Lie superalgebra $\mathfrakgl_M|N$, II: Quantum currents}},
author = {Lucia Bagnoli and Slaven Kožić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.12162},
eprint = {2608.12162},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.12162},
}
RIS
TY - UNPB
TI - Double Yangian and reflection algebras of the Lie superalgebra gl_M|N, II: Quantum currents
AU - Lucia Bagnoli
AU - Slaven Kožić
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.12162
UR - https://arxiv.org/abs/2608.12162
AB - In this paper, we continue our research on the double Yangian and reflection algebras of the Lie superalgebra gl_M|N. Extending the Etingof-Kazhdan construction, we introduce the structure of h-adic quantum vertex superalgebra on the vacuum module V^c(gl_M|N) over the double Yangian of level c∈ℂ. Next, we construct families of central elements in the completed double Yangian for gl_M|N at the critical level. Finally, we show that the level c restricted modules over the reflection algebra of gl_M|N are naturally equipped with the structure of quasi V^2c(gl_M|N)-module. By using this structure, we find explicit formulas for families of central elements in the completed reflection algebra of gl_M|N at the critical level.
ER -