SEMINAR: Groups and Combinatorics Seminar, Irreducible subgroups of classical algebraic groups
|Groups and Combinatorics Seminar, Irreducible subgroups of classical algebraic groups
Let G be a group, let H be a subgroup of G and let V be an irreducible KG-module over a field K. We say that (G,H,V) is an irreducible triple if V is an irreducible KH-module. Classifying the irreducible triples of a group is a fundamental problem in representation theory, with a long history and several applications.
The case where G is a simple algebraic group over an algebraically closed field can be traced back to work of Dynkin in the 1950s (H connected, char(K) = 0). Through work of Seitz and Testerman in the 1980s, and more recent work of Ghandour, the problem of determining the irreducible triples (G,H,V) for simple algebraic groups has essentially been reduced to the case where G is a classical group and H is disconnected.
In this talk I will report on recent work that determines all the irreducible triples (G,H,V) when G is classical and H is a disconnected, infinite, maximal subgroup. This is an important step towards a complete classification of the irreducible triples for simple algebraic groups. I will briefly recall some of the basic results on algebraic groups and representation theory that we will need, and I will describe some of the main ideas that are used in the proofs.
This is joint work with Soumaia Ghandour, Claude Marion and Donna Testerman.
Tim Burness (University of Southampton)
Weatherburn Lecture Theatre
Fri, 22 Mar 2013 15:00
Fri, 22 Mar 2013 16:00
Irene Pivotto <[email protected]>
Wed, 20 Mar 2013 10:32
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