Work

Complete reducibility: variations on a theme of Serre

Year: 2021

Type: article

Abstract: In this note, we unify and extend various concepts in the area of G-complete reducibility, where G is a reductive algebraic group. By results of Serre and Bate–Martin–Röhrle, the usual notion of G-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of G. We show that other variations of this notion, such as relative complete reducibility and $$\sigma $$ σ -complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.

Source: manuscripta mathematica

DOI: 10.1007/s00229-021-01318-2

Authors: Maike Gruchot, Alastair Litterick, Gerhard Röhrle

Institutions: RWTH Aachen University, University of Essex, Ruhr University Bochum

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,780

Funder: Ruhr-Universität Bochum