Geodesic
Orthogonal Subsets of Classical Root Systems and Coadjoint Orbits of Unipotent Groups
Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 65-80

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We consider a specific class of coadjoint orbits of maximal unipotent subgroups in classical groups over a finite field, i.e., 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.
Keywords: root system, polarization, Weyl group, irreducible representation, irreducible complex character, polarization of linear forms.
Mots-clés : coadjoint orbits, unipotent group 
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     author = {M. V. Ignat'ev},
     title = {Orthogonal {Subsets} of {Classical} {Root} {Systems} and {Coadjoint} {Orbits} of {Unipotent} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {65--80},
     publisher = {mathdoc},
     volume = {86},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a5/}
}
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M. V. Ignat'ev. Orthogonal Subsets of Classical Root Systems and Coadjoint Orbits of Unipotent Groups. Matematičeskie zametki, Tome 86 (2009) no. 1, pp. 65-80. http://geodesic.mathdoc.fr/item/MZM_2009_86_1_a5/