Lie Groups and Representation Theory

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2007/10/02

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
Pablo Ramacher (Gottingen University)


Invariant integral operators on affine G-varieties and their kernels
[ Abstract ]
We consider certain invariant integral operators on a smooth affine variety M carrying the action of a reductive algebraic group G, and assume that G acts on M with an open orbit. Then M is isomorphic to a homogeneous vector bundle, and can locally be described via the theory of prehomogenous vector spaces. We then study the Schwartz kernels of the considered operators, and give a description of their singularities using the calculus of b-pseudodifferential operators developed by Melrose. In particular, the restrictions of the kernels to the diagonal can be described in terms of local zeta functions.
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html