Root systems and the AtiyahSutcliffe problem
Abstract
In this short note, we show that the AtiyahSutcliffe conjectures for $n = 2m$, related to the unitary groups $U(2m)$, imply the author's analogous conjectures, which are associated with the symplectic groups $Sp(m)$. The proof is based on the simple fact that the root system of $U(2m)$ dominates that of $Sp(m)$.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 October 2019
 DOI:
 10.1063/1.5111442
 arXiv:
 arXiv:1903.00325
 Bibcode:
 2019JMP....60j1702M
 Keywords:

 Mathematics  Group Theory;
 Mathematical Physics;
 Mathematics  Metric Geometry;
 51Fxx;
 17B22
 EPrint:
 6 pages. Comments are welcome!