2024/06/03 by Westbury, Bruce W., Zinn-Justin, Paul
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2406.01348
The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. We give a uniform trigonometric R-matrix for the exceptional series in the representation L⊕ I, where L is the quantum deformation of the adjoint representation and I is the trivial representation. We construct a sixteen dimensional algebra, A^\square(\mathit2), which interpolates the algebras End(⊗2(L⊕ I)) and a 287 dimensional algebra, A^\square(\mathit3), which interpolates the algebras End(⊗3(L⊕ I)). The R-matrix lives in A^\square(\mathit2) and satisfies the Yang-Baxter equation in A^\square(\mathit3); it interpolates the trigonometric R-matrices for the points in the exceptional series.