This article is cited in 10 papers

Orthogonal Subsets of Classical Root Systems and Coadjoint Orbits of Unipotent Groups

M. V. Ignat'ev

Samara State University

Abstract: 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, coadjoint orbits, unipotent group, polarization, Weyl group, irreducible representation, irreducible complex character, polarization of linear forms.

UDC: 512.547.214+512.743.7

Received: 20.10.2008

DOI: 10.4213/mzm6356

 English version: Mathematical Notes, 2009, 86:1, 65–80

Bibliographic databases:

• 
• 
• 
•