$\mathrm{SO}(3)$-homogeneous decomposition of the flag scheme of $\mathrm{SL}_3$ over $\mathbb{Z}\left[1/2\right]$

Abstract

In this paper, we give Z [1 2]-forms of SO(3, C)-orbits in the flag variety of SL3(C). We also prove that they give a Z [1 2]-form of the KGB decomposition for SL3.

Algebraic approach to contraction families

“…Then the isomorphisms of ( 2) and (3) of Lemma 2.4 follow by generalities on the Galois descent (see [25,Theorem A.3]).…”