A cellular approach to the Hecke-Clifford superalgebra
arXiv:1401.1722
Abstract
The Hecke-Clifford superalgebra is a super-analogue of the Iwahori-Hecke algebra of type A. The classification of its simple modules is done by Brundan, Kleshchev and Tsuchioka using a method of categorification of affine Lie algebras. In this paper, we introduce another way to produce its simple modules with a generalized theory of cellular algebras which is originally developed by Graham and Lehrer. In our construction the key is that there is a right action of the Clifford superalgebra on the super-analogue of the Specht module. With the help of the notion of the Morita context, a simple module of the Hecke-Clifford superalgebra is made from that of the Clifford superalgebra.
[v2] 81 pages; corrected Corollary 6.41, added references and fixed typos. Thanks Tsuchioka-san. [v1] 77 pages