dorsal/arxiv
View SchemaHecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras
| Authors | L. K. Hadjiivanov, A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov, I. T. Todorov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712026 |
| URL | https://arxiv.org/abs/q-alg/9712026 |
| DOI | 10.1063/1.532779 |
| Journal | J.Math.Phys. 40 (1999) 427-448 |
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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"abstract": "The quantum dynamical Yang-Baxter (or Gervais-Neveu-Felder) equation defines\nan R-matrix R(p), where $p$ stands for a set of mutually commuting variables. A\nfamily of SL(n)-type solutions of this equation provides a new realization of\nthe Hecke algebra. We define quantum antisymmetrizers, introduce the notion of\nquantum determinant and compute the inverse quantum matrix for matrix algebras\nof the type R(p) a_1 a_2 = a_1 a_2 R. It is pointed out that such a quantum\nmatrix algebra arises in the operator realization of the chiral zero modes of\nthe WZNW model.",
"arxiv_id": "q-alg/9712026",
"authors": [
"L. K. Hadjiivanov",
"A. P. Isaev",
"O. V. Ogievetsky",
"P. N. Pyatov",
"I. T. Todorov"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1063/1.532779",
"journal_ref": "J.Math.Phys. 40 (1999) 427-448",
"title": "Hecke algebraic properties of dynamical R-matrices. Application to related quantum matrix algebras",
"url": "https://arxiv.org/abs/q-alg/9712026"
},
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