The Principal Symbol of Elliptic Differential Operators on Lie Groups and Homogeneous Spaces
摘要
We associate a principal symbol with elliptic differential operators acting on sections of vector fibrations over Lie groups and homogeneous spaces. This principal symbol is an element in the ring of virtual representations of the group, and, in particular instances, we show that it gives insights on the computation of spectral invariants linked to this type of operators.