Colloquium Lecture Department of Mathematics Bar Ilan University

Date: sunday 28 june '09, at 12:00 pm, Department Room

Speaker: Dr. Alexander Stasinski (Southampton)

Title: Unramified and Regular Representations

Abstract: The talk will be about two rather different constructions of smooth (complex) representations of certain compact p-adic groups. The first is a cohomological construction of so called unramified representations of reductive groups over finite local rings, and is a generalization of the classical construction of Deligne and Lusztig. This gives in particular a family of representations of any compact p-adic group of the form G(o), where G is a reductive group over the ring of integers o in a local non-Archimedean field. The second construction is a purely algebraic approach to the regular representations of GL_N(o), which is formally similar to the Bushnell-Kutzko construction of supercuspidal representations. We shall describe the main features of the constructions, and discuss some open questions regarding their overlap, that is, to what extent representations given by one construction are also given by the other.