Timeline for Commutator space of regular nilpotent elements

6 events

when toggle format	what		by	license	comment
Mar 2 at 18:27	comment	added	Torsten Schoeneberg		Does anything in the question mathoverflow.net/q/160891/27465 and/or its answers help here?
Jul 17, 2019 at 18:39	comment	added	Victor Protsak		I don't know the answer off-hand, but I'd like to point out that many properties of nilpotent elements and orbits are established on a case-by-case basis, with proofs in the exceptional cases also involving reduction to Levi components. The question itself appears close to Kostant's work on Toda lattices, which may be worth studying.
Jul 17, 2019 at 14:48	comment	added	YCor		I added "faithful" because the 1-dimensional trivial representation satisfies the condition and is clearly not what you're interested in. Also maybe you know whether the question reduces to the case of $\mathfrak{g}$ simple. Namely, if $\rho_i$ works for $\mathfrak{g}_i$, $i=1,2$, does $\rho_1\otimes\rho_2$ work for $\mathfrak{g}_1\times\mathfrak{g}_2$?
Jul 17, 2019 at 14:48	history	edited	YCor	CC BY-SA 4.0	added assumption to avoid trivial positive answer
Jul 17, 2019 at 14:38	history	edited	YCor	CC BY-SA 4.0	added reference to previous question, fixed subscript
Jul 17, 2019 at 13:56	history	asked	AThomas	CC BY-SA 4.0