Degenerate affine Hecke–Clifford algebras and type Q Lie superalgebras

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke–Clifford algebra (AHCA), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{H}_{\mathcal{C}\ell}^{{\rm aff}}(d)}$$\end{document}. Our construction includes an analogue of Zelevinsky’s segment representations, a complete combinatorial description of the simple calibrated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{H}_{\mathcal{C}\ell}^{{\rm aff}}(d)}$$\end{document}-modules, and a classification of the simple integral \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{H}_{\mathcal{C}\ell}^{{\rm aff}}(d)}$$\end{document}-modules. Our main tool is an analogue of the Arakawa–Suzuki functor for the Lie superalgebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{q}(n)}$$\end{document}.