Non-Abelian momentum polytopes for products of CP^2

Montaldi, James and Shaddad, Amna (2019) Non-Abelian momentum polytopes for products of CP^2. J. Geometric Mechanics. (In Press)

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Abstract

This is the first of two companion papers. The joint aim is to study a generalization to higher dimension of the point vortex systems familiar in 2-D. In this paper we classify the momentum polytopes for the action of the Lie group SU(3) on products of copies of complex projective 4-space. For 2 copies, the momentum polytope is simply a line segment, which can sit in the positive Weyl chamber in a number of ways. For a product of 3 copies there are 8 different types of generic momentum polytope for the product of 3 copies, and numerous transition polytopes, all of which are classified here. The different polytopes depend on the weights of the symplectic form on each copy of projective space. In the second paper we use reduction techniques to study the possible dynamics of interacting point vortices. The results are also applied to determine the inequalities satisfied by the sum of up to three 3x3 Hermitian matrices with double eigenvalues.

Item Type: Article
Uncontrolled Keywords: Momentum map, convex polyhedra, symplectic geometry, eigenvalues
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry
Depositing User: Dr James Montaldi
Date Deposited: 17 Jun 2019 20:51
Last Modified: 17 Jun 2019 20:51
URI: https://eprints.maths.manchester.ac.uk/id/eprint/2718

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