Darboux coordinates on the BFM spaces

Abstract

Bezrukavnikov-Finkelberg-Mirković [Compos. Math. {\bf 141} (2005)] identified the equivariant $K$-group of an affine Grassmannian, that we refer as (the coordinate ring of) a BFM space á là 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.

35pages, v2: added Appendix A on induction equivalence

References in corpus (3)

• Reconstruction and Convergence in Quantum $K$-Theory via Difference Equations
• Loop structure on equivariant $K$-theory of semi-infinite flag manifolds
• Chevalley formula for anti-dominant weights in the equivariant $K$-theory of semi-infinite flag manifolds