TY - GEN

T1 - Irreducible subgroups of simple algebraic groups - a survey

AU - Burness, Tim

AU - Testerman, Donna

PY - 2019/4/1

Y1 - 2019/4/1

N2 - Let G be a simple linear algebraic group over an algebraically closed field K of characteristic p > 0, let H be a proper closed subgroup of G and let V be a nontrivial finite dimensional irreducible rational KG-module. We say that (G, H, V ) is an irreducible triple if V is irreducible as a KH-module. Determining these triples is a fundamental problem in the representation theory of algebraic groups, which arises naturally in the study of the subgroup structure of classical groups.
In the 1980s, Seitz and Testerman extended earlier work of Dynkin on connected subgroups in characteristic zero to all algebraically closed fields. In this article we will survey recent advances towards a classification of irreducible triples for all
positive dimensional subgroups of simple algebraic groups.

AB - Let G be a simple linear algebraic group over an algebraically closed field K of characteristic p > 0, let H be a proper closed subgroup of G and let V be a nontrivial finite dimensional irreducible rational KG-module. We say that (G, H, V ) is an irreducible triple if V is irreducible as a KH-module. Determining these triples is a fundamental problem in the representation theory of algebraic groups, which arises naturally in the study of the subgroup structure of classical groups.
In the 1980s, Seitz and Testerman extended earlier work of Dynkin on connected subgroups in characteristic zero to all algebraically closed fields. In this article we will survey recent advances towards a classification of irreducible triples for all
positive dimensional subgroups of simple algebraic groups.

UR - https://www.cambridge.org/gb/academic/subjects/mathematics/algebra/groups-st-andrews-2017-birmingham?format=PB

M3 - Conference Contribution (Conference Proceeding)

SN - 9781108728744

T3 - London Mathematical Society Lecture Note Series

SP - 230

EP - 260

BT - Groups St Andrews 2017 in Birmingham

PB - Cambridge University Press

ER -