Twisted super Yangians of quasi-split type A

Abstract

We introduce the twisted super Yangian $Y^{\mathfrak{s}}_{\imath}$ of quasi-split type A in the Drinfeld current presentation for an arbitrary symmetric parity sequence $\mathfrak{s}$. We prove via Gauss decomposition that $Y^{\mathfrak{s}}_{\imath}$ is isomorphic to the special twisted super Yangian $\mathscr{SY}^{\mathfrak{s}}$, a subalgebra of the twisted super Yangian $\mathscr{Y}^{\mathfrak{s}}$ previously defined via the R-matrix presentation. As a corollary, we show that the algebras $Y^{\mathfrak{s}}_{\imath}$ corresponding to different symmetric parity sequences with the same $\mathfrak{m}$ and $\mathfrak{n}$ are isomorphic. We also establish a PBW theorem for $Y^{\mathfrak{s}}_{\imath}$ and describe the center of $\mathscr{Y}^{\mathfrak{s}}$ in terms of Gaussian generators, thereby generalizing known results for the nonsuper quasi-split type A case.