Hecke algebraic properties of dynamicalR-matrices. Application to related quantum matrix algebras
| Autor: | Ivan Todorov, Pavel Pyatov, L. K. Hadjiivanov, Oleg Ogievetsky, A. P. Isaev |
|---|---|
| Přispěvatelé: | Centre de Physique Théorique - UMR 6207 (CPT), Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), Ogievetsky, Oleg, Centre National de la Recherche Scientifique (CNRS)-Université de Toulon (UTLN)-Université de Provence - Aix-Marseille 1-Université de la Méditerranée - Aix-Marseille 2 |
| Rok vydání: | 1999 |
| Předmět: |
High Energy Physics - Theory
Pure mathematics Hecke algebra FOS: Physical sciences Type (model theory) 01 natural sciences High Energy Physics::Theory Matrix (mathematics) Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) 0101 mathematics Quantum Mathematical Physics Mathematics [MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA] [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] 010308 nuclear & particles physics Operator (physics) 010102 general mathematics Matrix mechanics Zero (complex analysis) Statistical and Nonlinear Physics High Energy Physics - Theory (hep-th) [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA] [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th] Realization (systems) |
| Zdroj: | Scopus-Elsevier |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.532779 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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