A note on the Tits systems of Kac-Moody Steinberg groups

Abstract

Let $G(H)$ be the Chevalley (Steinberg) Kac-Moody group of the Kac-Moody Lie algebra $L$. If $\sigma$ is the canonical homomorphism of $H$ onto $G$, and $\{B_{G}, N_{G}\}$ is the Tits system in $G$, then $\{\sigma^{-1}(B_{G}),\sigma^{-1}(N_{G})\}$ is a Tits system in the Weyl-simple subgroup of $H$.