2008/10/01 by Peter Tingley, Tingley, Peter
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT
paper · pdf · doi:10.48550/arxiv.0810.0088
9 pages. v2: minor corrections
openalex publication_date 2008/10/01 · arxiv created 2008/10/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Kirillov-Reshetikhin and Levendorskii-Soibelman developed a formula for the universal R-matrix of the form R=(X-1 ⊗ X-1) Δ(X). The action of X on a representation V permutes weight spaces according to the longest element in the Weyl group, so is only defined in finite type. We give a similar formula which is valid for the quantized universal enveloping algebra of any symmetrizable Kac-Moody algebra. This is done by replacing the action of X on V with an endomorphism that preserves weight spaces, but which is bar-linear instead of linear.