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Super duality and irreducible characters of orthosymplectic Lie superalgebras
 Invent. Math
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Howe Duality for Lie Superalgebras
 COMPOSITIO MATH
, 2000
"... We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicityfree decomposition of a symmetric and skewsymmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each ..."
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Cited by 26 (7 self)
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We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicityfree decomposition of a symmetric and skewsymmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicityfree decomposition into irreducible gl(mn)modules of the symmetric and skewsymmetric algebras of the symmetric square of the natural representation of gl(mn). In the former case we find as well explicit formulas for the highest weight vectors. Our work unifies and generalizes the classical results in symmetric and skewsymmetric models and admits several applications.
Euler characters and super Jacobi polynomials
 DEPARTMENT OF MATHEMATICAL SCIENCES, LOUGHBOROUGH UNIVERSITY, LOUGHBOROUGH
, 2009
"... We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi polynomials play a key role in the proof. ..."
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Cited by 4 (3 self)
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We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi polynomials play a key role in the proof.
Diagrams for perverse sheaves on isotropic Grassmannians and the supergroup SOSP(m2n)
, 2013
"... We describe diagrammatically a positively graded Koszul ... of type Dk 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 [Bra02]. The algebra is obtained by a ”folding ” pr ..."
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Cited by 3 (0 self)
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We describe diagrammatically a positively graded Koszul ... of type Dk 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 [Bra02]. 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(m2n)modules.
The generalized KacWakimoto conjecture and support varieties for the Lie superalgebra osp(m2n), arXiv eprints
, 1112
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