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Quasi-split symmetric pairs of $U(\mathfrak{gl}_N)$ and their Schur algebras

We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in Bao-Kujawa-Li-Wang (2018) specialized at $q=1$.