Yoshiki OSHIMA

Email oshima(
Representation theory, Lie group
Keywords Unitary representation, Lie group, D-module, branching law
Office Information Science and Technology C304 (Suita campus)

I am working on representations of Lie groups and related geometry, in particular, restriction and induction for infinite-dimensional representations of real reductive Lie groups. Although there are various approaches to the study of behavior of representations under restriction and induction, I have mainly considered D-module realization and a relation to the orbit method. When a Lie group acts on a manifold, its Lie algebra acts on the space of functions. As a generalization and abstraction of this action, a D-module gives a representation of Lie algebra. The correspondence between representations of Lie algebra and D-modules on the flag variety (Beilinson-Bernstein correspondence) can be applied to problems in the representation theory of Lie algebras and Lie groups. On the other hand, a relation between symplectic geometry (coadjoint orbit of Lie algebra) and representation theory has long been studied, which is called the orbit method. Recently, I am also interested in studying harmonic analysis and properties of representations by using the orbit method.