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

Abstract

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.

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

Cited by in corpus (2)

• Universal K-matrices for quantum Kac-Moody algebras
• A half-twist type formula for the R-matrix of a symmetrizable Kac-Moody algebra