Integral Presentations for the Universal R-matrix

Details Integral Presentations for the Universal R-matrix Integral Presentations for the Universal R-matrix

2000-08-30

arxiv.org/abs/math/0008226v1

Mathematics

Quantum Algebra

19 pages, LaTeX 2.09 using amssym.def and amssym.tex

Scientific paper

We present an integral formula for the universal R-matrix of quantum affine algebra 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 $U_q(\hat{sl}_2)$ 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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