Orthogonal subsets of root systems and the orbit method

Details Orthogonal subsets of root systems and the orbit method Orthogonal subsets of root systems and the orbit method

2010-07-29

arxiv.org/abs/1007.5220v3

St. Petersburg Math. J., 22 (2011), no. 5, pp. 777-794

Mathematics

Representation Theory

16 pages

Scientific paper

Let $k$ be the algebraic closure of a finite field, $G$ a Chevalley group over $k$, $U$ the maximal unipotent subgroup of $G$. To each orthogonal subset $D$ of the root system of the group $G$ and each set $\xi$ of $|D|$ non-zero scalars from $k$ one can assign the coadjoint orbit of the group $U$. We prove that the dimension of such an orbit does not depend on $\xi$. We also give an upper bound of the dimension in terms of the Weyl group.

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