Kirwan polyhedron of holomorphic coadjoint orbits

TL;DR

This paper computes the explicit affine equations describing the moment polyhedron of holomorphic coadjoint orbits for certain Hermitian Lie groups using geometric invariant theory methods.

Contribution

It introduces a novel approach to describe the moment polyhedron of holomorphic coadjoint orbits via GIT techniques and affine equations.

Findings

Explicit affine equations for the moment polyhedron are derived.

The method applies to Hermitian symmetric spaces of noncompact type.

Provides a new computational tool for understanding coadjoint orbits.

Abstract

Let G be a simple, noncompact, connected, real Lie group with finite center, and K a maximal compact subgroup of G. We assume that G/K is Hermitian. Using GIT methods derived from the generalized eigenvalue problem, we compute a set of affine equations describing the moment polyhedron of the projection on k* of holomorphic coadjoint orbits of G.