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Spherical birational sheets in reductive groups · arXivDesk

2008.13508Aug 31, 202029 pages

Spherical birational sheets in reductive groups

Filippo Ambrosio, Mauro Costantini

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 $G$

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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 O₁, O₂ 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 O₁ and O₂ are isomorphic as G-modules.

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The paper addresses: Spherical birational sheets in reductive groups.
We classify the spherical birational sheets in a complex simple simply-connected algebraic group.