扩展扭曲\(h\)-杨式代数的不变量
Invariants of the extended twisted $h$-Yangian
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中文总结 AI 辅助
研究扩展扭曲\(h\)-杨式代数\({\rm Y}_{N,h}^{\text{tw}}\)，通过展示其具有特定代数的限制模和拟模结构，利用量子Feigin - Frenkel中心元素得出中心元素、不变量公式及交换族等贡献。
中文摘要 AI 辅助
我们研究扩展扭曲\(h\)-杨式代数\({\rm Y}_{N,h}^{\text{tw}}\)，它有正交和辛\(h\)-杨式代数作为其商代数。我们表明\({\rm Y}_{N,h}^{\text{tw}}\)自然具有特定代数\({\rm DY}_{N,h,c}^{tw}\)（类似于量子对偶）的限制模结构，以及与\(A\)型三角\(R\)-矩阵相关的Etingof - Kazhdan量子仿射顶点代数的\(\phi\)-坐标拟模结构。最后，我们展示量子Feigin - Frenkel中心的元素如何产生\({\rm DY}_{N,h,c}^{tw}\)中心元素和临界水平\({\rm Y}_{N,h}^{\text{tw}}\)不变量的显式公式，以及正交和辛\(h\)-杨式代数中的交换族。
英文摘要
We investigate the extended twisted $h$-Yangian ${\rm Y}_{N,h}^{\text{tw}}$, a certain algebra which admits both the orthogonal and the symplectic $h$-Yangian as its quotients. We show that ${\rm Y}_{N,h}^{\text{tw}}$ is naturally equipped with the structure of restricted module for a certain algebra ${\rm DY}_{N,h,c}^{tw}$, which resembles the quantum double, as well as with the structure of $ϕ$-coordinated quasi module for the Etingof-Kazhdan quantum affine vertex algebra associated with the trigonometric $R$-matrix of type $A$. Finally, we demonstrate how the elements of the quantum Feigin--Frenkel center give rise to explicit formulas for central elements of ${\rm DY}_{N,h,c}^{tw}$ and invariants of ${\rm Y}_{N,h}^{\text{tw}}$ at the critical level, as well as to commutative families in the orthogonal and symplectic $h$-Yangians.
