Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras
q-alg
2009-10-30 v1 High Energy Physics - Theory
Quantum Algebra
Abstract
The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines an R-matrix R(p), where 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.
Keywords
Cite
@article{arxiv.q-alg/9712026,
title = {Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras},
author = {L. K. Hadjiivanov and A. P. Isaev and O. V. Ogievetsky and P. N. Pyatov and I. T. Todorov},
journal= {arXiv preprint arXiv:q-alg/9712026},
year = {2009}
}
Comments
28 pages, LaTeX