Hecke–Clifford Superalgebras and Crystals of Type <em>D</em>_<em>l</em>⁽²⁾

Abstract

In [BK], Brundan and Kleshchev showed that some parts of the representation theory of the affine Hecke–Clifford superalgebras and its finite-dimensional “cyclotomic” quotients are controlled by the Lie theory of type A_2_l(2) when the quantum parameter q is a primitive (2_l_ + 1)-th root of unity. We show that similar theorems hold when q is a primitive 4_l_-th root of unity by replacing the Lie theory of type A_2_l(2) with that of D__l(2).