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

L. K. Hadjiivanov·A. P. Isaev·O. V. Ogievetsky·P. N. Pyatov·I. T. Todorov
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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.

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L. K. Hadjiivanov, A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov, I. T. Todorov. 1997-12-10. Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras. https://doi.org/10.1063/1.532779

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