Steinberg slices and group-valued moment maps
Representation Theory
2022-09-19 v3 Algebraic Geometry
Symplectic Geometry
Abstract
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 relative compactification 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.
Cite
@article{arxiv.2103.14704,
title = {Steinberg slices and group-valued moment maps},
author = {Ana Balibanu},
journal= {arXiv preprint arXiv:2103.14704},
year = {2022}
}
Comments
v3: Final version. v2: Small improvement to main theorem, minor revisions for clarity