Title: Progenerators of Bernstein blocks

Abstract: Let F be a non-archimedean local field and G be a connected reductive group over F. For a Bernstein block in the category of smooth complex representations of G(F), we have two kinds of progenerators: the compactly induced representation ind_K^G(rho) of a type (K, rho), and the parabolically induced representation I_P^G(Pi^M) of a progenerator Pi^M of a Bernstein block for a Levi subgroup M of G. In this talk, we construct an explicit isomorphism of these two progenerators. We also explain that the induced isomorphism between the endomorphism algebras is compatible with their descriptions in terms of affine Hecke algebras.