1
$\begingroup$

Borho in this paper showed that a sheet (i.e. a suitable union of adjoint orbits of the same dimension) in a complex semisimple Lie algebra $\mathfrak{g}$ is classified by a pair $(\mathfrak{l},O)$ where $\mathfrak{l}$ is a Levi subalgebra of $\mathfrak{g}$ and $O$ is a rigid nilpotent orbit of $\mathfrak{l}$.

How does the story go in the case of a sheet in the corresponding group $G$? I guess I need to replace the Levi algebra with a pseudo-Levi group. I'd appreciate if you could suggest a reference to look at.

Improve this question
$\endgroup$
1

1 Answer 1

Reset to default
1
$\begingroup$

There is a paper by Carnovale and Esposito, see 1011.5791. As the comment section of the link says, it seems to go back to Lusztig.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Sorry for the oversight. I think I noticed the first version of this preprint but didn't go back to it. (As they point out in their addendum, some of the ideas involved were introduced earlier by Lusztig). I'm not sure how far this analogue of the Lie algebra case goes. Probably the mild restriction on characteristic is there mainly to get a natural bijection between the nilpotent orbits and unipotent classes as in characteristic 0 $\endgroup$
    – Jim Humphreys
    Dec 6, 2011 at 0:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.