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

2013/10/07 by Ehrig, Michael, Stroppel, Catharina · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1310.1972

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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• Quantum Howe duality and Schur duality of type AIII

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