Representation theory for Iwahori-Hecke algebras and Schur algebras of classical type

We develop a theory of support varieties for Iwahori-Hecke algebras of type A, which detects natural homological properties such as the complexity of modules. Furthermore, we extend the theory to Hecke algebras of classical type with the help of Morita equivalences between Iwahori-Hecke algebras of classical type.Schur algebras of classical type are centralizer algebras of the action of Hecke algebras of classical type on tensor spaces. We give an isomorphism theorem between Schur algebras of type B and type A, which enables us to address the questions of cellularity, quasi-hereditariness and representation type of Schur algebras of type B, and also discuss possible approach to generalize the result to type D.