Twisted super Yangians of type AIII and their representations

Abstract

We study the super analogue of the Molev-Ragoucy reflection algebras, which we call twisted super Yangians of type AIII, and classify their finite-dimensional irreducible representations under certain conditions. These superalgebras are coideal subalgebras of the super Yangian $\mathcal{Y}({\mathfrak{gl}}_{m|n})$ and are associated with symmetric pairs of type AIII in Cartan's classification. We establish the Schur-Weyl type duality between degenerate affine Hecke algebras of type BC and twisted super Yangians.

arXiv comment44 pages. v2 submitted version; v3 final version with updated references

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