Representation Theory Seminar

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"Stabilizers of Actions on Projective Space"

Today we will fill in a gap in our previous discussions, proving that every linear algebraic group embeds as a closed subgroup of a general linear group. This will follow from a key theorem of Chevalley relating subgroups of a linear algebraic group to fixed points of actions of that group on projective spaces. Having already seen a relation between solvable subgroups and stabilizers of actions of the group on full flag varieties we will begin to see more generally how one can translate representation theoretic data into algebro-geometric data and vice-versa.

MC 5413