Integral Presentations for the Universal R-matrix

2000/08/30 by J. Ding, Ding, J., S. Khoroshkin +3
Mathematics · #17B37 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:17B37 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0008226

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

arxiv created 2000/08/30 · arxiv updated 2009/11/30

Abstract

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(sl₂) 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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