G-complete reducibility, geometric invariant theory and spherical buildings Michael Bate, Benjamin Martin, Gerhard Röhrle

Format:

Book

Author/Creator:

Bate, Michael (Michael Edward), author.

Martin, Benjamin (Professor in mathematics), author.

Röhrle, Gerhard, author.

Series:

Oberwolfach seminars ; 57.

Oberwolfach seminars 2296-5041 volume 57

Language:

English

Subjects (All):

Representations of groups.

Buildings (Group theory).

Group algebras.

Physical Description:

1 online resource

Place of Publication:

Cham, Switzerland Birkhäuser [2026]

Summary:

"The aim of this textbook is to introduce readers at a graduate level to G-complete reducibility and explain some of its many applications across pure mathematics. It is based on the Oberwolfach Seminar of the same name which took place in 2022.The notion of G-complete reducibility for subgroups of a reductive algebraic group is a natural generalisation of the notion of complete reducibility in representation theory. Since its introduction in the 1990s, complete reducibility has been widely studied, both as an important concept in its own right, with applications to the classification and structure of linear algebraic groups, and also as a useful tool with applications in representation theory, geometric invariant theory, the theory of buildings, and number theory"-- Springer Nature Link

Contents:

Geometric invariant theory

G-complete reducibility : first definitions and properties

The geometric approach

Finiteness, rationality and rigidity results

The spherical building of G

The optimality formalism

Applications to G-complete reducibility

Large versus small characteristic

G-complete reducibility over an arbitrary field

Variations, applications and future directions

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (De Gruyter Brill, viewed June 11, 2026)

Other Format:

Print version Bate, Michael (Michael Edward) G-complete reducibility, geometric invariant theory and spherical buildings

ISBN:

9783032088666

3032088666

OCLC:

1594452552

Access Restriction:

Restricted for use by site license