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

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. On leave of absence from: Division of Theoretical Physics, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria; e-mail address: lhadji@inrne.acad.bg On leave of absence from: Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141 980 Moscow Region, Russia; e-mail address: isaevap@thsun1.jinr.ru 3 On leave of absence from: P.N. Lebedev Physical Institute, Theoretical Department, 117924 Moscow, Leninsky prospect 53, Russia; e-mail address: oleg@cpt.univ-mrs.fr e-mail address: pyatov@thsun1.jinr.ru On leave of absence from: Division of Theoretical Physics, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, BG-1784 Sofia, Bulgaria; e-mail address: todorov@inrne.acad.bg