Symmetric subgroup schemes

TL;DR

This paper constructs subgroup schemes within Chevalley group schemes that parametrize symmetric subgroups of reductive groups, utilizing quantum symmetric pairs to enable quantization and quantum subgroup constructions.

Contribution

It introduces a novel method to parametrize symmetric subgroups via subgroup schemes, connecting classical and quantum group theories.

Findings

Construction of closed subgroup schemes parametrizing symmetric subgroups.

Development of quantum coisotropic subgroups in quantized function algebras.

Establishment of a link between classical symmetric subgroups and quantum group structures.

Abstract

Chevalley group schemes are group schemes defined over the integers that parametrize connected reductive groups over algebraically closed fields as geometric fibers. In this paper, we construct closed subgroup schemes of Chevalley group schemes that parametrize symmetric subgroups of reductive groups as geometric fibers. Our construction relies crucially on the theory of quantum symmetric pairs and thus naturally admits a quantization. At the quantum level, this leads to the construction of coisotropic quantum right subgroups of the quantized function algebras of reductive groups.