On Samelson products in $SU(n)$-and $Sp(n)$

Abstract

Let $a$ and $b$ be two positive integers such that $a,b<n$. We denote the inclusion $\Sigma \mathbb{C}{P}^a\to SU(n)$ by ${\epsilon }_{a,n}$. Also, let $m$ and $n$ be two positive integers such that $m<n$. This article has two parts. In the first part, we will study the order of the Samelson product $⟨{\epsilon }_{a,n},{\epsilon }_{b,n}⟩$ where $a+b=n+k$, for $k\ge 0$. Also, we will give two applications. In the second part, we will study the order of the Samelson product $S^{4m-1}\wedge Q_{n-m+1}\to Sp(n)$, where $Q_{n-m+1}$ is the symplectic quasi-projective space of rank $n-m+1$.

arXiv comment23 pages. arXiv admin note: text overlap with arXiv:2305.11447