[see also: straight]
Let us now prove directly (without recourse to [5]) that ......
It should be possible to prove this directly by studying the fixed point set of the action of $G$.
They were defined directly by Lax [2], essentially as we have defined them.
In the remainder of this section, we study some properties of $K$, with the eventual aim (not realized yet) of describing $K$ directly using $G$.
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