Extensions of graded affine Hecke algebra modules

In this dissertation, we study extensions of graded ane Hecke algebra modules. In particular, based on an explicit projective resolution on graded ane Hecke algebra modules, we prove a duality result for Ext-groups. This duality result with analysis on some parabolically induced modules gives a new proof of the fact that all higher Ext-groups between discrete series vanish. Finally, we study a twisted Euler-Poincare pairing and show the pairing depends on the Weyl group structure of graded ane Hecke algebra modules.