Hecke Algebras of Type Bn at Roots of Unity

Abstract

The simple modules for Hecke algebras of type Bn were constructed, under certain restrictions on the characteristic of the field, in [7]. Using new ideas, introduced by the third-named author for Hecke algebras of type An [13], we now remove these restrictions on the characteristic. We present a collection of modules, of which the non-zero ones form a complete set of pairwise non-isomorphic simple modules. In addition, we formulate a conjecture as to which of the modules are non-zero.