The primary purpose of this memoir is to give a realization of the representation [italic]U of a locally compact group [italic]G, induced from a representation [italic]L of a closed subgroup [italic]H, on a continuous sum of Banach spaces over the coset space [italic]G/[italic]H.
Let [italic]V be a finite dimensional vector space over an algebraically closed field of characteristic p [greater than] 0 and let G = SL([italic]V), Sp([italic]V), or SO([italic]V). The main result describes all closed, connected, overgroups of [italic]X in SL([italic]V), assum…
Let [italic]Y be a simply-connected, simple algebraic group of exceptional type, defined over an algebraically closed field [italic]k of prime characteristic [italic]p > 0. The main result describes all semisimple, closed connected subgroups of [italic]Y which act irreducibly on…