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arxiv 1310.1972 v3 pith:K4RB5TV2 submitted 2013-10-07 math.RT math.QAmath.RA

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

Michael Ehrig , Catharina Stroppel This is my paper
classification math.RT math.QAmath.RA
keywords algebrassubalgebrascategorycoidealdualityendomorphismfamilyhowe
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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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  1. On a symplectic quantum Howe duality

    math.RT 2023-03 unverdicted novelty 7.0

    Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.