Relations among presentations of quantum affine superalgebras

Determine the specific relations connecting the Drinfeld–Jimbo, Drinfeld, and R-matrix presentations of quantum affine superalgebras and establish the corresponding isomorphisms among these presentations.

Background

Quantum affine algebras admit multiple presentations—Drinfeld–Jimbo, Drinfeld (current), and R-matrix—and extensive work has established isomorphisms among these presentations in the non-super (bosonic) setting and for some special super cases. However, for general quantum affine superalgebras, the precise interrelations among these presentations remain incompletely characterized.

This paper develops the R-matrix presentation for the quantum affine superalgebra associated with the orthosymplectic Lie superalgebra osp(2m+1|2n) and proves an isomorphism with the Drinfeld presentation, thereby extending known results. Despite this progress in a specific family, the broader program of describing explicit relations and isomorphisms among the Drinfeld–Jimbo, Drinfeld, and R-matrix presentations across quantum affine superalgebras remains open.