2026/07/18 by Kang Lu
Mathematics · #math.RT #math.QA
We introduce the twisted super Yangian Y^\mathfraks\imath of quasi-split type A in the Drinfeld current presentation for an arbitrary symmetric parity sequence \mathfraks. We prove via Gauss decomposition that Y^\mathfraks\imath is isomorphic to the special twisted super Yangian \mathscrSY^\mathfraks, a subalgebra of the twisted super Yangian \mathscrY^\mathfraks previously defined via the R-matrix presentation. As a corollary, we show that the algebras Y^\mathfraks\imath corresponding to different symmetric parity sequences with the same \mathfrakm and \mathfrakn are isomorphic. We also establish a PBW theorem for Y^\mathfraks\imath and describe the center of \mathscrY^\mathfraks in terms of Gaussian generators, thereby generalizing known results for the nonsuper quasi-split type A case.