Let G be a connected reductive group over a field F. A twisted Levi subgroup G0 of G is a reductive subgroup such that G' [circle times]F F[over-bar] is a Levi subgroup of G' [circle times]F F[over-bar]. Twisted Levi subgroups have been an important tool in studying the structure theory of representations of p-adic groups. For example, supercuspidal representations are built out of certain representations of twisted Levi subgroups ([20]), and Hecke algebra isomorphisms are established with Hecke algebras on twisted Levi subgroups, which suggests an inductive structure of representations (see [9] for example).National Science Foundation (U.S.). Focused Research Grou
