Enhanced adjoint actions and their orbits for the general linear group

Kyo Nishiyama and Takuya Ohta

Vol. 298 (2019), No. 1, 141–155

DOI: 10.2140/pjm.2019.298.141

Abstract

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.

Keywords

enhanced nilpotent cone, exotic nilpotent cone, adjoint quotient, classical invariant theory

Mathematical Subject Classification 2010

Primary: 14L30

Secondary: 15A72, 16W22

Milestones

Received: 19 March 2018

Accepted: 6 June 2018

Published: 2 February 2019