Note on Samelson products in exceptional Lie groups

TL;DR

This paper investigates the non-triviality of Samelson products in certain p-localized exceptional Lie groups, completing the classification for cases with p-torsion free homology.

Contribution

It provides a complete determination of the (non-)triviality of Samelson products in specific exceptional Lie groups at certain primes, extending previous results.

Findings

Determined Samelson product triviality for (E_7,5) and (E_7,7).

Established non-triviality for (E_8,7).

Completed classification for p-torsion free homology cases.

Abstract

We determine (non-)triviality of Samelson products of inclusions of factors of the mod $p$ decomposition of $G_{(p)}$ for $(G,p)=(E_7,5),(E_7,7),(E_8,7)$. This completes the determination of (non-)triviality of those Samelson products in $p$-localized exceptional Lie groups when $G$ has $p$-torsion free homology.