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

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

1997-12-10

arxiv.org/abs/q-alg/9712026v1

J.Math.Phys. 40 (1999) 427-448

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, LaTeX

Scientific paper

10.1063/1.532779

The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R(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 R(p) a_1 a_2 = a_1 a_2 R. It is pointed out that such a quantum matrix algebra arises in the operator realization of the chiral zero modes of the WZNW model.

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