S. Tsuchioka: Hecke–Clifford Superalgebras and Crystals of Type D_l^(2)



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
DOI: 10.2977/PRIMS/13

Link to article

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_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

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