# Enhanced adjoint action and their orbits for the general linear group

## TL;DR

This paper investigates the enhanced adjoint action of the general linear group on a combined space of Lie algebra and representations, characterizing regular semisimple orbits and the structure of the enhanced null cone.

## Contribution

It provides a detailed analysis of the orbit structure and null cone for the enhanced adjoint action, including irreducible components and their dimensions.

## Key findings

- Classification of regular semisimple orbits
- Description of the enhanced null cone structure
- Determination of irreducible components and their dimensions

## Abstract

We studied 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 determined regular semisimple orbits (i.e., closed orbits of maximal dimension) and the structure of enhanced null cone, including its irreducible components and their dimensions.