Eigencone, saturation and Horn problems for symplectic and odd orthogonal groups

TL;DR

This paper addresses the eigenvalue and intersection problems for symplectic and odd orthogonal groups, providing solutions to the Horn and saturation problems specific to these classical groups.

Contribution

It extends the Horn and saturation problem solutions to symplectic and odd orthogonal groups, which were previously unresolved.

Findings

Solved the Horn problem for symplectic and odd orthogonal groups.

Established saturation theorems for these groups.

Developed intersection theory for associated homogeneous spaces.

Abstract

We consider the eigenvalue problem and the associated intersection theory of homogenous spaces for the symplectic and odd orthogonal groups. We solve the Horn and saturation problems for these classical groups.