Speaker
Toshihisa Kubo
(Ryukoku University)
Description
Let X be a smooth manifold and Y a smooth submanifold of X. Take G'⊂G to be a pair of Lie groups that act on Y⊂X, respectively. We call a differential operator D between the space of smooth sections for a G-equivariant vector bundle over X and that for a G'-equivariant vector bundle over Y a differential symmetry breaking operator (differential SBO for short) if D is G'-intertwining. The F-method is a powerful machinery on the classification and construction of differential SBOs. It allows one to classify and construct differential SBOs by solving a certain system of partial differential equations. The key idea is the Fourier transform of the generalized Verma modules. In this talk we shall overview the F-method in an elementary manner.