Re: the parabolic subgroups of SO(n,C)

James Dolan wrote:

given sufficient interest i might be convinced to spell out in a later
post a detailed intuitive picture of the 4 basic parabolic subgroups
of so(2,3) (which is equivalent to so(5) when working over the complex
numbers), in terms of the "incidence geometry of extension of partial
isometries" as briefly described below.)

I'd certainly be interested to hear more about this,
though I did not follow your account completely.

we know from special relativity that a pseudo-euclidean vector space
of signature (1,3) is a helpful auxiliary device for studying
isometries from a euclidean vector space v of dimension 1 (aka "time")
to a euclidean vector space w of dimension 3 (aka "space"), because
the graph of such an isometry can be thought of as a "light-like"
subspace of the pseudo-euclidean vector space v+w (aka "space-time").

Wouldn't an isometry from E^1 to E^3
just correspond to steady motion along a straight line?
Or do I misunderstand what you mean by isometry?

--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
.

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