Isomorphism between the R-matrix and Drinfeld presentations of quantum affine algebra: Type C

An explicit isomorphism between the R-matrix and Drinfeld presentations of the quantum affine algebra in type A was given by Ding and Frenkel [Commun. Math. Phys. 156, 277-300 (1993)]. We show that this result can be extended to types B, C, and D and give a detailed construction for type C in this paper. In all classical types, the Gauss decomposition of the generator matrix in the R-matrix presentation yields the Drinfeld generators. To prove that the resulting map is an isomorphism, we follow the work of Frenkel and Mukhin [Sel. Math. 8, 537-635 (2002)] in type A and employ the universal R-matrix to construct the inverse map. A key role in our construction is played by a homomorphism theorem, which relates the quantum affine algebra of rank n - 1 in the R-matrix presentation with a subalgebra of the corresponding algebra of rank n of the same type.