Heat Kernel Asymptotics on Homogeneous Bundles

Details Heat Kernel Asymptotics on Homogeneous Bundles Heat Kernel Asymptotics on Homogeneous Bundles

2007-08-01

arxiv.org/abs/0708.0234v1

Int.J.Geom.Meth.Mod.Phys.5:1-23,2008

Mathematics

Differential Geometry

29 pages, Proceedings of the 2007 Midwest Geometry Conference in Honor of Thomas P. Branson

Scientific paper

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal solution correctly reproduces the exact heat kernel diagonal after a suitable regularization and analytical continuation.

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