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

Paul-Emile Paradan

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.

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

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.
Paper Structure (10 sections, 6 theorems, 15 equations)

This paper contains 10 sections, 6 theorems, 15 equations.

Table of Contents

  1. Introduction
  2. An application of the O'Shea-Sjamaar Theorem
  3. Complexification and antiholomorphic involution
  4. Orthogonal projection
  5. O'Shea-Sjamaar's Theorem
  6. Horn inequalities
  7. Inequalities determining $\mathcal{A}(p,q)$
  8. Examples
  9. Computation of $\mathcal{A}(2,2)$
  10. Computation of $\mathcal{A}(3,3)$

Key Result

Lemma 2.1

Let $X,X'\in \mathfrak{u}(n)$.

Theorems & Definitions (10)

  • Lemma 2.1
  • Theorem 2.2
  • Definition 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Remark 2.6
  • Remark 2.7
  • Proposition 3.1
  • Proposition 3.2
  • Remark 3.3