Degenerate Affine Hecke-Clifford Algebras and Type $Q$ Lie Superalgebras

Details Degenerate Affine Hecke-Clifford Algebras and Type $Q$ Lie Superalgebras Degenerate Affine Hecke-Clifford Algebras and Type $Q$ Lie Superalgebras

2009-04-03

arxiv.org/abs/0904.0499v3

Mathematics

Representation Theory

66 pages. Section 8 revised

Scientific paper

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA). Our construction includes an analogue of Zelevinsky's segment representations, a complete combinatorial description of the simple calibrated modules, and a classification of the simple integral modules. Additionally, we construct an analogue of the Arakawa-Suzuki functor for the Lie superalgebra of type Q.

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