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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).
LECTURES ON SPIN REPRESENTATION THEORY OF SYMMETRIC GROUPS
"... The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes, we present a coherent account of the spin counterparts of se ..."
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The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes, we present a coherent account of the spin counterparts of several classical constructions such as the Frobenius characteristic map, Schur duality, the coinvariant algebra, Kostka polynomials, and Young’s seminormal form. 1.
Frobenius character formula and spin generic degrees for HeckeClifford algebra
, 1201
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A cellular approach to the Hecke–Clifford superalgebra
"... The Hecke–Clifford superalgebra is a superanalogue of the Iwahori–Hecke algebra of type A. The classification of its simple modules is done by Brundan, Kleshchev and Tsuchioka using a method of categorification of affine Lie algebras. In this paper, we introduce another way to produce its simple mo ..."
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The Hecke–Clifford superalgebra is a superanalogue of the Iwahori–Hecke algebra of type A. The classification of its simple modules is done by Brundan, Kleshchev and Tsuchioka using a method of categorification of affine Lie algebras. In this paper, we introduce another way to produce its simple modules with a generalized theory of cellular algebras which is originally developed by Graham and Lehrer. In our construction the key is that there is a right action of the Clifford superalgebra on the superanalogue of the Specht module. With the help of the notion of the Morita context, a simple module of the Hecke–Clifford superalgebra is made from that of the Clifford superalgebra.