A Drinfeld Presentation of the Queer Super-Yangian

Abstract

We introduce a Drinfeld presentation for the super-Yangian $\mathrm{Y}(\mathfrak{q}_n)$ associated with the queer Lie superalgebra $\mathfrak{q}_n$. The Drinfeld generators of $\mathrm{Y}(\mathfrak{q}_n)$ are obtained through a block Gauss decomposition of the generator matrix in its RTT presentation, and the Drinfeld relations are explicitly computed by utilizing a block version of its RTT relations. As a byproduct, we obtain a new expression for the central series of $\mathrm{Y}(\mathfrak{q}_n)$ in terms of Gauss generators.