ENHANCED ADJOINT ACTIONS AND THEIR ORBITS FOR THE GENERAL LINEAR GROUP

摘要

We study an enhanced adjoint action of the general linear group on a product of its Lie algebra and a vector space consisting of several copies of defining representations and its duals. We determine regular semisimple orbits (i.e., closed orbits of maximal dimension) and the structure of enhanced null cone, including its irreducible components and their dimensions.