SEMINAR: Groups and Combinatorics Seminar: Phill Schultz, 4pm Aug 2 in Weatherburn LT

Speaker: Phill Schultz (University of Western Australia)

Title: Actions of Aut(V) on linearly independent subsets of a vector space V

Time and place: 4pm Friday 02 Aug 2019, Weatherburn LT

Abstract: Let V be a finite dimensional rational vector space. The action of the general linear group Aut(V) on the set of bases of V is the main content of First Year Linear Algebra, so you might think there can be nothing new to say about it; but the subject still holds a few surprises.

For example, if G is a subgroup of V, the stabilizer of G in Aut(V) acts on the set of maximal linearly independent subsets of V contained in G. The orbits of this action determine the indecomposable decompositions of G.

Furthermore, the stabilizer of the set of subgroups of V containing G as a subgroup of finite index acts transitively on a larger set of linearly independent subsets, and this action determines a coarse structure theorem for G.