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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.
Degenerate affine HeckeClifford algebras and type Q Lie superalgebras
, 2009
"... We construct the finite dimensional simple integral modules for the (degenerate) affine HeckeClifford algebra (AHCA), Haff Cℓ (d). Our construction includes an analogue of Zelevinsky’s segment representations, a complete combinatorial description of the simple calibrated Haff Cℓ (d)modules, and ..."
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Cited by 8 (2 self)
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We construct the finite dimensional simple integral modules for the (degenerate) affine HeckeClifford algebra (AHCA), Haff Cℓ (d). Our construction includes an analogue of Zelevinsky’s segment representations, a complete combinatorial description of the simple calibrated Haff Cℓ (d)modules, and a classification of the simple integral Haff Cℓ (d)modules. Our main tool is an analogue of the ArakawaSuzuki functor for the Lie superalgebra q(n).
Generalized trace and modified dimension functions on ribbon categories
 Selecta Math., Volume 17, Issue
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PatureauMirand  Ambidextrous objects and trace functions for nonsemisimple categories
 Proc. Amer. Math. Soc
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1 SUPPORT VARIETIES AND REPRESENTATIONS OF TAME BASIC CLASSICAL LIE SUPERALGEBRAS
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