A formula for the R-matrix using a system of weight preserving endomorphisms

Details A formula for the R-matrix using a system of weight preserving endomorphisms A formula for the R-matrix using a system of weight preserving endomorphisms

2007-11-30

arxiv.org/abs/0711.4853v3

Represent. Theory 14 (2010), 435-445

Mathematics

Representation Theory

11 pages. v2: expanded introduction and background. v3 edits for clarity. To appear in Representation theory, an electronic jo

Scientific paper

We give a formula for the universal R-matrix of the quantized universal enveloping algebra $U_q(\g).$ This is similar to a previous formula due to Kirillov-Reshetikhin and Levendorskii-Soibelman, except that where they use the action of the braid group element $T_{w_0}$ on each representation, we show that one can instead use a system of weight preserving endomorphisms. One advantage of our construction is that it is well defined for all symmetrizable Kac-Moody algebras. However we have only established that the result in equal to the universal R-matrix in finite type.

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