On the h-adic Quantum Vertex Algebras Associated with Hecke Symmetries

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 V c ( R ) via the Etingof–Kazhdan construction, while, in the braided case, they produce ( ϕ -coordinated) V c ( R ) -modules. Next, we show that the coefficients of suitably defined quantum determinant can be used to obtain central elements of V c ( R ) , as well as the invariants of such ( ϕ -coordinated) V c ( R ) -modules. Finally, we investigate a certain algebra which is closely connected with the representation theory of V c ( R ) .