Deformation quantization of coadjoint orbits


Shilin Yu

15:10 - 16:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In 1960s, Kirillov proposed that irreducible unitary representations of a Lie group should be obtained by quantizing the coadjoint orbits of the Lie algebra as symplectic manifolds via geometric quantization. The case of noncompact semisimple groups has remained unsettled due to lack of invariant polarizations on the orbits. Inspired by the work of Gukov and Witten, we propose a new way to quantize coadjoint orbits using hyperkahler structures on the orbits and deformation quantization. Part of the project is joint work in progress with Conan Leung.