Quantization of Hamiltonian LG-spaces
Speaker: Yiannis Loizides, University of Toronto
Abstract: I will describe work in progress with E. Meinrenken and Y. Song. We construct a spin-c structure on a finite-dimensional "cross-section" of a Hamiltonian LG-space. The corresponding Dirac operator has a well-defined index in the completion of the representation ring of the maximal torus. (This "quantization" is closely related to the quantization scheme for quasi-Hamiltonian G-spaces via twisted K-theory proposed by E. Meinrenken a few years ago.) We study the multiplicities by deforming the operator with a suitable vector field. A quantization-commutes-with-reduction result follows from an interesting inequality just involving certain Lie-algebra data.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:35pm - 3:30pm