论文标题
在$ h $ - 亚种量子顶点代数与Hecke对称性相关的代数
On the $h$-adic quantum vertex algebras associated with Hecke symmetries
论文作者
论文摘要
我们研究了Gurevich和Saponov引入的Hecke Symetries，研究RTT型Yangians的量子顶点代数框架以及与Hecke Symetries相关的编织的Yangians。首先，我们为上述类似扬式的代数构建了几个模块系列，在RTT类型的情况下，它们导致一定的$ h $ h $ h $ - ad量的量子Quantum vartex代数$ \ nathcal {v} _c（r）$ agraidof-kazhdan construction $ coce（$ con） $ \ MATHCAL {V} _C（R）$ - 模块。接下来，我们表明，适当定义的量子决定因素的系数可用于获得$ \ nathcal {v} _c（r）$的中心元素，以及此类（$ ϕ $ coordined）$ \ nathcal {v} _c（v} _c（r）$ - 模块的不变性。最后，我们研究了与$ \ Mathcal {v} _C（r）$的表示理论密切相关的某个代数。
We study the quantum vertex algebraic framework for the Yangians of RTT-type and the braided Yangians associated with Hecke symmetries, introduced by Gurevich and Saponov. First, we construct several families of modules for the aforementioned Yangian-like algebras which, in the RTT-type case, lead to a certain $h$-adic quantum vertex algebra $\mathcal{V}_c (R)$ via the Etingof-Kazhdan construction, while, in the braided case, they produce ($ϕ$-coordinated) $\mathcal{V}_c (R)$-modules. Next, we show that the coefficients of suitably defined quantum determinant can be used to obtain central elements of $\mathcal{V}_c (R)$, as well as the invariants of such ($ϕ$-coordinated) $\mathcal{V}_c (R)$-modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of $\mathcal{V}_c (R)$.
