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