Brian Hall, University of Notre Dame
Berezin-Toeplitz quantization on Lie groups
The generalized Segal-Bargmann transform is a unitary map from $L^2$ of a compact group onto a certain $L^2$ space of holomorphic functions on the associated complex group. On the compact group side, one can perform Schrodinger-style quantization of symbols with polynomial behavior in the momentum variables, obtaining differential operators on the compact group. I will show how such operators, when conjugated by the Segal-Bargmann transform, can be expressed as Toeplitz operators. This shows the relationship between Schrodinger and Berezin-Toeplitz quantization in this case.