Mechanics on flag manifolds

Abstract

We study the connection between $\mathrm{SU}(n)$ spin chains and one-dimensional sigma models on flag manifolds. Using this connection, we calculate the spectrum of the Laplace-Beltrami operator and geodesics for a particular class of metrics on ${\mathbb{CP}}^1$ and ${\mathcal{F}}_3$, which is a manifold of complete flags in ${\mathbb{C}}^3$.

7 pages, prepared as a contribution to `SQS-24'