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.

28 pages, LaTeX

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Cited by in corpus (13)

• Spectral extension of the quantum group cotangent bundle
• Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model
• Quantum matrix algebra for the SU(n) WZNW model
• Braids, Shuffles and Symmetrizers
• R-matrix realization of two-parameter quantum group U_{r,s}(gl_n)
• Chiral zero modes of the SU(n) Wess-Zumino-Novikov-Witten model
• Quantum su(n)_k monodromy matrices
• Differential Calculus on h-Deformed Spaces
• Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners
• Zero modes of the SU(2)_k Wess-Zumino-Novikov-Witten model in Euler angles parametrization
• Dynamical quantum determinants and Pfaffians
• On the $h$-adic quantum vertex algebras associated with Hecke symmetries
• Generalized homologies for the zero modes of the SU(2) WZNW model