Hecke-Clifford superalgebras and crystals of type \(D_l^{(2)}\) (Q983319)

Previously, Brundan and Kleshchev have shown 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 \(A_{2l}^{(2)}\) when the quantum parameter \(q\) is a primitive \((2l+1)\)th root of unity. In this paper the author shows that similar theorems hold when \(q\) is a primitive \(4l\)th root of unity by replacing the Lie theory of type \(A_{2l}^{(2)}\) with that of \(D_l^{(2)}\).