李超代数$\boldsymbol{\frak{gl}_{M|N}}$的双重杨代数与反射代数，II：量子流
Double Yangian and reflection algebras of the Lie superalgebra $\mathfrak{gl}_{M|N}$, II: Quantum currents
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中文总结 AI 辅助
本文研究李超代数$\frak{gl}_{M|N}$的双重杨代数与反射代数，构造临界水平双重杨代数的中心元，推广Etingof-Kazhdan构造引入量子顶点超代数结构，证明反射代数限制模的准模性质。
中文摘要 AI 辅助
本文继续开展李超代数$\frak{gl}_{M|N}$的双重杨代数与反射代数研究，首先构造临界水平下$\frak{gl}_{M|N}$双重杨代数的中心元族；接着推广Etingof-Kazhdan构造，在水平$c \times \times \times$（$c \times \times \times$为复数）的$\frak{gl}_{M|N}$双重杨代数的真空模$V^c(\frak{gl}_{M|N})$上引入$h$-adic量子顶点超代数结构；最后证明$\frak{gl}_{M|N}$反射代数的限制模自然具备准$V^c(\frak{gl}_{M|N})$模结构。
英文摘要
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.
发表机构
- Dipartimento di Matematica, Sapienza Università di Roma（罗马大学数学系）
- INFN sezione di Roma（罗马意大利国家核物理研究所）
- University of Zagreb Faculty of Science, Department of Mathematics（萨格勒布大学理学院数学系）
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