Odd primary homotopy types of $\mathrm{SU}(n)$–gauge groups

Abstract

Let ${\mathcal{G}}_k\left(SU\left(n\right)\right)$ be the gauge group of the principal $SU\left(n\right)$–bundle with second Chern class $k$. If $p$ is an odd prime and $n\le {\left(p-1\right)}^2+1$, we classify the $p$–local homotopy types of ${\mathcal{G}}_k\left(SU\left(n\right)\right)$.