Representations of Convolution Algebras
Our primary goal in this chapter is to obtain a classification of simple modules over the affine Hecke algebra H although the techniques we develop works in much greater generality (we will indicate this on several occasions). In §8.1 we introduce a class of “standard” H-modules. In the same section we define simple H-modules in terms of a certain intersection form on standard module, and formulate the main classification theorem for simple H-modules. After a short overview of derived categories of constructible sheaves and intersection cohomology, given in §§8.3–8.4, we will express in §8.5 the underlying vector space of a simple H-module in terms of the intersection cohomology.