Affine slice for the coadjoint action of a class of biparabolic subalgebras of a semisimple Lie algebra

TL;DR

This paper constructs an explicit affine slice for the coadjoint action of certain biparabolic subalgebras of semisimple Lie algebras, including all Borel subalgebras, simplifying the understanding of their orbit structure.

Contribution

It provides a simple explicit construction of an affine slice for the coadjoint action of biparabolic subalgebras, extending to all Borel subalgebras.

Findings

Explicit affine slice construction for biparabolic subalgebras

Includes all Borel subalgebras as special cases

Simplifies analysis of coadjoint orbits

Abstract

In this article, we give a simple explicit construction of an affine slice for the coadjoint action of a certain class of biparabolic (also called seaweed) subalgebras of a semisimple Lie algebra over an algebraically closed field of characteristic zero. In particular, this class includes all Borel subalgebras.