Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups. (English. Russian original) Zbl 1182.20041
Math. Notes 86, No. 1, 65-80 (2009); translation from Mat. Zametki 86, No. 1, 65-80 (2009).
Summary: We consider a specific class of coadjoint orbits of maximal unipotent subgroups in classical groups over a finite field; namely, orbits associated with orthogonal subsets in root systems. We derive a formula for the dimension of these orbits in terms of the Weyl group and construct polarizations for canonical forms on the orbits. As a consequence, we describe all possible dimensions of irreducible representations of such unipotent groups.
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 17B22 | Root systems |
| 20G40 | Linear algebraic groups over finite fields |
Keywords:
root systems; coadjoint orbits; dimensions of orbits; unipotent groups; Weyl groups; irreducible representations; irreducible complex characters; polarizations of linear forms; classical groups over finite fieldsReferences:
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