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 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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- January 1999
- DOI:
- 10.1063/1.532779
- arXiv:
- arXiv:q-alg/9712026
- Bibcode:
- 1999JMP....40..427H
- Keywords:
-
- 03.65.Fd;
- 11.10.Lm;
- 02.10.Sp;
- Algebraic methods;
- Nonlinear or nonlocal theories and models;
- Mathematics - Quantum Algebra;
- High Energy Physics - Theory
- E-Print:
- 28 pages, LaTeX