Root systems and the Atiyah-Sutcliffe problem
In this short note, we show that the Atiyah-Sutcliffe 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 $Sp(m)$.
Journal of Mathematical Physics
- Pub Date:
- October 2019
- Mathematics - Group Theory;
- Mathematical Physics;
- Mathematics - Metric Geometry;
- 6 pages. Comments are welcome!