Hecke algebraic properties of dynamical R -matrices. Application to related quantum matrix algebras

Abstract

The quantum dynamical Yang–Baxter (or Gervais–Neveu–Felder) equation defines an R-matrix R̂(p), where p stands for a set of mutually commuting variables. A family of SL(n)-type solutions of this equation provides a new realization of the Hecke algebra. We define quantum antisymmetrizers, introduce the notion of quantum determinant and compute the inverse quantum matrix for matrix algebras of the type R̂(p)a1a2=a1a2R̂. It is pointed out that such a quantum matrix algebra arises in the operator realization of the chiral zero modes of the WZNW model.