On the $h$-adic quantum vertex algebras associated with Hecke symmetries

Abstract

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 ($\varphi$-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 ($\varphi$-coordinated) ${\mathcal{V}}_c(R)$-modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of ${\mathcal{V}}_c(R)$.

23 pages, comments are welcome

References in corpus (2)

• $(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated quasi modules for nonlocal vertex algebras
• $h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\varphi$-coordinated modules