Twisted super Yangians of quasi-split type A

Abstract

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

38 pages, to appear in Journal of Algebra