Integral presentations for the Universal R-Matrix

J. Ding; S. Khoroshkin; S. Pakuliak

doi:10.1023/A:1026730817516

Integral presentations for the Universal R-Matrix

J. Ding^*, S. Khoroshkin, S. Pakuliak

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We present an integral formula for the universal R-matrix of quantum affine algebra U_q(ĝ) with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper configuration spaces. For general g we conjecture that such cycles exist and unique. For U_q(sl₂) we describe precisely the cycles and present a new simple expression for the universal R-matrix as a result of calculation of corresponding integrals.

Original language	English
Pages (from-to)	121-141
Number of pages	21
Journal	Letters in Mathematical Physics
Volume	53
Issue number	2
DOIs	https://doi.org/10.1023/A:1026730817516
Publication status	Published - 2 Jul 2000
Externally published	Yes

Keywords

Quantized affine algebras
Universal R-matrix

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Ding, J., Khoroshkin, S., & Pakuliak, S. (2000). Integral presentations for the Universal R-Matrix. Letters in Mathematical Physics, 53(2), 121-141. https://doi.org/10.1023/A:1026730817516

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N2 - We present an integral formula for the universal R-matrix of quantum affine algebra Uq(ĝ) with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper configuration spaces. For general g we conjecture that such cycles exist and unique. For Uq(sl2) we describe precisely the cycles and present a new simple expression for the universal R-matrix as a result of calculation of corresponding integrals.

AB - We present an integral formula for the universal R-matrix of quantum affine algebra Uq(ĝ) with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper configuration spaces. For general g we conjecture that such cycles exist and unique. For Uq(sl2) we describe precisely the cycles and present a new simple expression for the universal R-matrix as a result of calculation of corresponding integrals.

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Integral presentations for the Universal R-Matrix

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