Hecke–Clifford Superalgebras and Crystals of Type D_l^(2)
by Shunsuke Tsuchioka
Research Institute for Mathematical Sciences, Kyoto University, 606-8502, KYOTO, JAPAN
Publications of the Research Institute for Mathematical Sciences
Volume 46, Issue 2, 2010, pp. 423–471
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_2l^(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 typeA_2l^(2) with that of D_l^(2).
Keywords: Hecke–Cliﬀord superalgebras, symmetric groups, spin representations, modular branching rule, Lie theory, quantum groups, Kashiwara’s crystal, categoriﬁcation
Source: Publications of the Research Institute for Mathematical Sciences, http://www.ems-ph.org/journals/journal.php?jrn=prims