Steinberg slices and group-valued moment maps

Seminar: 
Geometry, Symmetry and Physics
Event time: 
Monday, April 11, 2022 - 4:30pm
Location: 
Zoom
Speaker: 
Ana Balibanu
Speaker affiliation: 
Harvard University
Event description: 

We define a class of transversal slices in spaces which are quasi-Poisson for the action of a complex semisimple group G. This is a multiplicative analogue of Whittaker reduction. One example is the multiplicative universal centralizer of G, which is equipped with the usual symplectic structure in this way. We construct a smooth partial compactification of Z by taking the closure of each centralizer fiber in the wonderful compactification of G. By realizing this partial compactification as a transversal in a larger quasi-Poisson variety, we show that it is smooth and log-symplectic.