Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups
| Autor: | M. V. Ignat’ev |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Classical group
Pure mathematics Weyl group General Mathematics Root system Unipotent symbols.namesake Finite field Irreducible representation symbols FOS: Mathematics Canonical form Astrophysics::Earth and Planetary Astrophysics Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory Mathematics |
| DOI: | 10.48550/arxiv.0904.2841 |
| Popis: | 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 $k$. Comment: 11 pages |
| Databáze: | OpenAIRE |
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