Orthosymplectic R-matrices

Abstract We present a formula for trigonometric orthosymplectic R -matrices associated with any parity sequence and establish their factorization into the ordered product of q -exponents parametrized by positive roots in the corresponding reduced root systems. The latter is crucially based on the construction of orthogonal bases of the positive subalgebra through q -bracketings and combinatorics of dominant Lyndon words, as developed in Clark et al. (Quantum Topol 7(3):553–638, 2016). We further evaluate the affine orthosymplectic R -matrices, establishing their intertwining property as well as matching them with those obtained through the Yang–Baxterization technique of Ge et al. (Int J Mod Phys A 6(21):3735–3779, 1991). This reproduces the celebrated formulas of Jimbo (Commun Math Phys 102(4):537–547, 1986) for classical BCD types and the formula of Mehta et al. (J Phys A 39(1):17–26, 2006) for the standard parity sequence.