Kepler Problem and Bound/Unbound Duality

In Riemannian geometry, there is a well-known compact/non compact duality for symmetric spaces, which says, for example, the 2-sphere S^2 is the compact dual of the upper half complex plane H^2. In this talk, we will report a strikingly-similar duality in symplectic geometry for which superminimal co-adjoint orbit and adjoint group play the role of symmetric space and projective group respectively. This new duality is a corollary of the speaker’s very recent work on Kepler problem (i.e. the mathematical model for the simplest solar system or atom). If time permits, a similar duality in representation theory will be reported as well.

An extenced abstract can be download here.