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Mar 7, 2013 at 21:21 comment added Jim Humphreys @Ben: For applications to tangent (or cotangent) bundles it's important to be clear about where dualization in the Lie algebra is needed. But in the Lie algebra setting the Killing form is helpful, and the duals of the various finite dimensional representations involved are easy enough to handle.
Mar 7, 2013 at 20:12 comment added Ben McKay @MTS: yes, dual of the nilradical. But classification of the $P$-invariant subspaces of the nilradical gives those of its dual, and vice versa, so good enough.
Mar 7, 2013 at 16:07 comment added MTS Isn't $\mathfrak{g}/\mathfrak{p}$ isomorphic to the dual of the nilradical of $\mathfrak{p}$?
Mar 7, 2013 at 13:02 comment added Vít Tuček Sorry for the jargon. I've edited my "answer" accordingly.
Mar 7, 2013 at 13:01 history edited Vít Tuček CC BY-SA 3.0
fixed reference
Mar 7, 2013 at 3:27 comment added Sasha What is "parabook"?
Mar 6, 2013 at 21:08 history answered Vít Tuček CC BY-SA 3.0