Publications of the Research Institute for Mathematical Sciences
Full-Text PDF (615 KB) | Metadata | Table of Contents | PRIMS summary
Published online: 2010-06-07
Hecke–Clifford Superalgebras and Crystals of Type Dl(2)Shunsuke Tsuchioka (1) Kyoto University, Japan
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 A2l(2) when the quantum parameter q is a primitive (2l + 1)-th root of unity. We show that similar theorems hold when q is a primitive 4l-th root of unity by replacing the Lie theory of type A2l(2) with that of Dl(2).
Keywords: Hecke–Cliﬀord superalgebras, symmetric groups, spin representations, modular branching rule, Lie theory, quantum groups, Kashiwara’s crystal, categoriﬁcation
Tsuchioka Shunsuke: Hecke–Clifford Superalgebras and Crystals of Type Dl(2). Publ. Res. Inst. Math. Sci. 46 (2010), 423-471. doi: 10.2977/PRIMS/13