Degenerate Affine Hecke-clifford Algebras and Type Q Lie Superalgebras

@inproceedings{Kujawa2009DegenerateAH,
title={Degenerate Affine Hecke-clifford Algebras and Type Q Lie Superalgebras},
author={Jonathan R. Kujawa and Joshua Sussan},
year={2009}
}

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of the Arakawa-Suzuki functor for the Lie superalgebra q(n).