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<p>We present a formula for trigonometric orthosymplectic <i>R</i>-matrices associated with any parity sequence and establish their factorization into the ordered product of <i>q</i>-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 <i>q</i>-bracketings and combinatorics of dominant Lyndon words, as developed in&#xa0;Clark et al. (Quantum Topol 7(3):553–638, 2016). We further evaluate the affine orthosymplectic <i>R</i>-matrices, establishing their intertwining property as well as matching them with those obtained through the Yang–Baxterization technique of&#xa0;Ge et al. (Int J Mod Phys A 6(21):3735–3779, 1991). This reproduces the celebrated formulas of&#xa0;Jimbo (Commun Math Phys 102(4):537–547, 1986) for classical BCD types and the formula of&#xa0;Mehta et al. (J Phys A 39(1):17–26, 2006) for the standard parity sequence.</p>

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Orthosymplectic R-matrices

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  • 发表日期：

    2026年5月15日

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  • Kyungtak Hong,
  • Alexander Tsymbaliuk

摘要

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.