so consider the maximal parabolic subalgebra of g2 indicated by abcfgjkp in the root system picture below:

===a===
b=c=d=e
=f=g=h=
j=k=m=n
===p===

now what are the ideals in this subalgebra?

-,bj,bfj,bcfjk,abcfgjk ???

then is the quotient algebra by the ideal bj isomorphic to the triangle-shaped maximal parabolic subalgebra of b2? if so then what does this mean? is there a nice "geometric interpretation" of this (in a certain sense that i'm vaguely imagining...)?

then also the quotient by bfj, and a maximal parabolic of a2 ... ??...

and what _about_ the relationship between ideals and invariant distributions here?? ... or something... ??...

??the relationship between the ideals of a2,b2,g2(,...???) should translate into a relationship between invariant distributions?? ??or something??...

hmm, wait a minute... certainly the cartan subalgebra has a continuum of ideals in general... ??perhaps somewhat typical for a lot of larger subalgebras as well... ??...

...but still...