Drinfeld Realization for Quantum Affine Orthosymplectic Superalgebras

Abstract

A well-defined braid groupoid action is an essential tool for constructing the new Drinfeld realization of a quantum affine superalgebra. For quantum affine orthosymplectic superalgebras (types B, C, and D), this action was not fully defined, as the braid operators $T_i$ were known only up to normalization factors. In this paper, we solve this problem by providing the explicit formulas for these operators for any choice of parity. This yields a well-defined braid group action on the direct sum of these superalgebras. As a consequence, we use this action to formally introduce the new Drinfeld realization $U_q^D({\hat{\mathfrak{g}}}_s)$ for these types and prove that the corresponding Drinfeld-Jimbo quantum group $U_q({\hat{\mathfrak{g}}}_s)$ is its surjective homomorphic image. We conjecture that this map is an isomorphism.

34 pages