Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

Details Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups

2009-04-18

arxiv.org/abs/0904.2841v3

Math. Notes, 86 (2009), no. 1, pp. 65-80

Mathematics

Representation Theory

11 pages

Scientific paper

Let $\Phi$ be a classical root system and $k$ be a field of sufficiently large characteristic. Let $G$ be the classical group over $k$ with the root system $\Phi$, $U$ be its maximal unipotent subgroup and $\mathfrak{u}$ be the Lie algebra of $U$. Let $D$ be an orthogonal subset of $\Phi$ and $\Omega$ be a coadjoint orbit of $U$ associated with $D$. We construct a polarization of $\mathfrak{u}$ at the canonical form on $\Omega$. We also find the dimension of $\Omega$ in terms of the Weyl group of $\Phi$. As a corollary, we determine all possible dimensions of irreducible complex represenations of the group $U$ for the case of finite field $k$.

Affiliated with

Also associated with

No associations

Rating

Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-546029