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

Ludmil Hadjiivanov | Zendy; A. P. Isaev | Zendy; O. Ogievetsky | Zendy; Pavel Pyatov | Zendy; Иван Тодоров | Zendy

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

Author(s) -

Ludmil Hadjiivanov,

A. P. Isaev,

O. Ogievetsky,

Pavel Pyatov,

Иван Тодоров

Publication year - 1999

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.532779

Subject(s) - realization (probability) , mathematics , pure mathematics , matrix (chemical analysis) , quantum , quantum group , algebra over a field , operator algebra , mathematical physics , quantum algebra , operator (biology) , type (biology) , algebra representation , quantum mechanics , physics , statistics , materials science , composite material , ecology , biochemistry , chemistry , repressor , biology , gene , transcription factor

The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation definesan R-matrix R(p), where $p$ stands for a set of mutually commuting variables. Afamily of SL(n)-type solutions of this equation provides a new realization ofthe Hecke algebra. We define quantum antisymmetrizers, introduce the notion ofquantum determinant and compute the inverse quantum matrix for matrix algebrasof the type R(p) a_1 a_2 = a_1 a_2 R. It is pointed out that such a quantummatrix algebra arises in the operator realization of the chiral zero modes ofthe WZNW model.Comment: 28 pages, LaTe

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