Isomorphism between the R-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types B and D

Abstract

Following the approach of Ding and Frenkel [Comm. Math. Phys. 156 (1993), 277-300] for type A, we showed in our previous work [J. Math. Phys. 61 (2020), 031701, 41 pages] that the Gauss decomposition of the generator matrix in the R-matrix presentation of the quantum affine algebra yields the Drinfeld generators in all classical types. Complete details for type C were given therein, while the present paper deals with types B and D. The arguments for all classical types are quite similar, so we mostly concentrate on the necessary additional details specific to the underlying orthogonal Lie algebras.