Finiteness of orbits and poles of intertwining operators

Xiaoxiang Yu, Purdue University

Abstract

For a maximal parabolic subgroup P = MN of a connected reductive algebraic group G defined over a p-adic field F, using an extension of Gaussian Elimination, it is shown that in the case when N is abelian the center and twisted center of a representative from an open orbit in N under Ad(M) are equal. This makes it possible to determine the poles of standard intertwining operators and connect them to orbital integrals and endoscopy. When G is a classical group and using the same technique, it is also proved that for half the maximal parabolic subgroups P = MN, Lie(N) is a reducible, prehomogeneous vector space under Ad(M). This will lead to similar results in these cases when N is not necessary Abelian.

Degree

Ph.D.

Advisors

Shahidi, Purdue University.

Subject Area

Mathematics

COinS