Darboux coordinates on the BFM spaces
Representation Theory
2020-12-23 v2 Algebraic Geometry
Quantum Algebra
Abstract
Bezrukavnikov-Finkelberg-Mirkovi\'c [Compos. Math. {\bf 141} (2005)] identified the equivariant -group of an affine Grassmannian, that we refer as (the coordinate ring of) a BFM space \'a l\`a Teleman [Proc. ICM Seoul (2014)], with a version of Toda lattice. We give a new system of generators and relations of a certain localization of this space, that can be seen as a version of its Darboux coordinate. This establishes a conjecture in Finkelberg-Tymbaliuk [Progress in Math. {\bf 300} (2019)] that relates the BFM space of a connected reductive algebraic group with those of Levi subgroups.
Keywords
Cite
@article{arxiv.2008.01310,
title = {Darboux coordinates on the BFM spaces},
author = {Syu Kato},
journal= {arXiv preprint arXiv:2008.01310},
year = {2020}
}
Comments
35pages, v2: added Appendix A on induction equivalence