78 research outputs found
Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra
We give a proof of a Schur-Weyl duality statement between the Brauer algebra
and the ortho-symplectic Lie superalgebra .Comment: 22 pages, minor changes, to appear in M
Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m|2n)
We describe diagrammatically a positively graded Koszul algebra \mathbb{D}_k
such that the category of finite dimensional \mathbb{D}_k-modules is equivalent
to the category of perverse sheaves on the isotropic Grassmannian of type D_k
constructible with respect to the Schubert stratification. The connection is
given by an explicit isomorphism to the endomorphism algebra of a projective
generator described in by Braden. The algebra is obtained by a "folding"
procedure from the generalized Khovanov arc algebras. We relate this algebra to
the category of finite dimensional representations of the orthosymplectic
supergroups. The proposed equivalence of categories gives a concrete
description of the categories of finite dimensional SOSP(m|2n)-modules
Projective-injective modules, Serre functors and symmetric algebras
We describe Serre functors for (generalisations of) the category O associated
with a semi-simple complex Lie algebra. In our approach, projective-injective
modules play an important role. They control the Serre functor in the case of a
quasi-hereditary algebra having a double centraliser property with respect to a
symmetric algebra. As an application of the double centraliser property and our
description of Serre functors, we prove three conjectures of Khovanov about the
projective-injective modules in the parabolic category O for sl_n
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