dorsal/arxiv
View SchemaBraid group approach to the derivation of universal \v{R} matrices
| Authors | Feng Pan, Lianrong Dai |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712038 |
| URL | https://arxiv.org/abs/q-alg/9712038 |
| DOI | 10.1088/0305-4470/29/18/031 |
| Journal | Journal of Physics A: Math. Gen. 29(1996),6043-6057 |
Abstract
A new method for deriving universal \v{R} matrices from braid group representation is discussed. In this case, universal \v{R} operators can be defined and expressed in terms of products of braid group generators. The advantage of this method is that matrix elements of \v{R} are rank independent, and leaves multiplicity problem concerning coproducts of the corresponding quantum groups untouched. As examples, \v{R} matrix elements of $[1]\times [1]$, $[2]\times [2]$, $[1^{2}]\times [1^{2}]$, and $[21]\times [21]$ with multiplicity two for $A_{n}$, and $[1]\times [1]$ for $B_{n}$, $C_{n}$, and $D_{n}$ type quantum groups, which are related to Hecke algebra and Birman-Wenzl algebra, respectively, are derived by using this method.
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"abstract": "A new method for deriving universal \\v{R} matrices from braid group\nrepresentation is discussed. In this case, universal \\v{R} operators can be\ndefined and expressed in terms of products of braid group generators. The\nadvantage of this method is that matrix elements of \\v{R} are rank independent,\nand leaves multiplicity problem concerning coproducts of the corresponding\nquantum groups untouched. As examples, \\v{R} matrix elements of $[1]\\times\n [1]$, $[2]\\times [2]$, $[1^{2}]\\times [1^{2}]$, and $[21]\\times [21]$ with\nmultiplicity two for $A_{n}$, and $[1]\\times [1]$ for $B_{n}$,\n $C_{n}$, and $D_{n}$ type quantum groups, which are related to Hecke algebra\nand Birman-Wenzl algebra, respectively, are derived by using this method.",
"arxiv_id": "q-alg/9712038",
"authors": [
"Feng Pan",
"Lianrong Dai"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1088/0305-4470/29/18/031",
"journal_ref": "Journal of Physics A: Math. Gen. 29(1996),6043-6057",
"title": "Braid group approach to the derivation of universal \\v{R} matrices",
"url": "https://arxiv.org/abs/q-alg/9712038"
},
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