Comments on an article by Fomin, Fulton, Li, and Poon

TL;DR

This paper withdraws a previous note due to an incorrect calculation that contradicted earlier results, clarifying the description of the cone A(p,q) and its relation to existing theorems.

Contribution

It corrects a previous miscalculation and clarifies the relationship between the cone A(p,q) description and the O'Shea-Sjamaar theorem.

Findings

Correction of the previous calculation error.

Refinement of the cone A(p,q) description.

Clarification of the relation to O'Shea-Sjamaar theorem.

Abstract

We withdraw this note because our calculation of the A(3,3) example, which initially contradicted one of the results of a 2005 paper by Fomin-Fulton-Li-Poon, was incorrect. In the second version of the prepublication arXiv:2303.11653, we explain how the description of the cone A(p,q) obtained by Fomin-Fulton-Li-Poon refines that obtained using the O'Shea-Sjamaar theorem.