Spherical birational sheets in reductive groups

DOI10.1016/J.JALGEBRA.2021.07.036arXiv2008.13508MaRDI QIDQ6348070

Mauro Costantini, Filippo Ambrosio

Publication date: 31 August 2020

Abstract: We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when $G$ is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes $mathcal{O}_1$, $mathcal{O}_2$ of $G$ lie in the same birational sheet, up to a shift by a central element of $G$, if and only if the coordinate rings of $mathcal{O}_1$ and $mathcal{O}_2$ are isomorphic as $G$-modules. As a consequence, we prove a conjecture of Losev for the spherical subvariety of the Lie algebra of $G$.

Mathematics Subject Classification ID

Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Compactifications; symmetric and spherical varieties (14M27)

This page was built for publication: Spherical birational sheets in reductive groups

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6348070)