Publications of the Research Institute for Mathematical Sciences


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Volume 46, Issue 2, 2010, pp. 423–471
DOI: 10.2977/PRIMS/13

Published online: 2010-06-07

Hecke–Clifford Superalgebras and Crystals of Type Dl(2)

Shunsuke Tsuchioka[1]

(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