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arXiv · 1310.1972

Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality

Michael Ehrig·Catharina Stroppel
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Abstract

We describe how certain cyclotomic Nazarov-Wenzl algebras occur as endomorphism rings of projective modules in a parabolic version of BGG category O of type $D$. Furthermore we study a family of subalgebras of these endomorphism rings which exhibit similar behaviour to the family of Brauer algebras even when they are not semisimple. The translation functors on this parabolic category O are studied and proven to yield a categorification of a coideal subalgebra of the general linear Lie algebra. Finally this is put into the context of categorifying skew Howe duality for these subalgebras.

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Michael Ehrig, Catharina Stroppel. 2013-10-07. Nazarov-Wenzl algebras, coideal subalgebras and categorified skew Howe duality. https://arxiv.org/abs/1310.1972

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