Root Systems and the Atiyah-Sutcliffe Problem

Joseph Malkoun

doi:10.1063/1.5111442

paper

Root Systems and the Atiyah-Sutcliffe Problem

arXiv:1903.00325 · doi:10.1063/1.5111442

Abstract

In this short note, we show that the Atiyah-Sutcliffe conjectures for $n = 2 m$ , related to the unitary groups $U (2 m)$ , imply the author's analogous conjectures, which are associated with the symplectic groups $S p (m)$ . The proof is based on the simple fact that the root system of $U (2 m)$ dominates that of $S p (m)$ .

6 pages. Comments are welcome!