Dept Math & Stat UiT, Forskningsparken B459

10 May 2023 Wed 14:00-15:00

Henrik Winther (UiT)

"Minimal projective orbits of semi-simple Lie groups"

Let G be a Lie group with representation R on a real simple G-module V. We will call the orbits of the induced action of R on the projectivization PV the projective orbits, and projective orbits of lowest possible dimension will be called minimal. We show that when G is semi-simple and non-compact, there exists a compact subgroup K in G such that the minimal orbits of G are in bijection with the minimal K-orbits on a K-invariant proper subspace W in V. In the case that G is split-real, K is the trivial subgroup and there is a unique closed projective orbit, which is moreover of minimal dimension.