A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution
Symplectic Geometry
2023-11-02 v2 Differential Geometry
Representation Theory
Abstract
In this note we show that the multiplicative Grothendieck-Springer space has a natural quasi-Poisson structure. The associated group-valued moment map is the resolution morphism, and the quasi-Hamiltonian leaves are the connected components of the preimages of Steinberg fibers. This is a multiplicative analogue of the standard Poisson structure on the additive Grothendieck-Springer resolution, and an explicit illustration of a more general procedure of reduction along Dirac realizations which is developed in recent work of the author and Mayrand.
Keywords
Cite
@article{arxiv.2210.07195,
title = {A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution},
author = {Ana Balibanu},
journal= {arXiv preprint arXiv:2210.07195},
year = {2023}
}