Index of parabolic and seaweed subalgebras of son

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9 Scopus citations

Abstract

The index of a Lie algebra r is defined as min w∈r*dim rw, where rw is the stabilizer of w under the coadjoint action of r on r*. In this paper we derive simple formulas for the index of parabolic subalgebras of the even orthogonal algebra g=so(2n,k). We use these formulas to prove the conjecture that indq<n for any parabolic subalgebra or seaweed subalgebra (intersection of two weakly opposite parabolics) q of so(2n,k). Some partial results for subalgebras of g=so(2n+1,k) are also obtained.

Original languageEnglish (US)
Pages (from-to)127-142
Number of pages16
JournalLinear Algebra and Its Applications
Volume374
DOIs
StatePublished - Nov 15 2003

Keywords

  • Frobenius Lie algebra
  • Lie algebra index
  • Parabolic subalgebras
  • Seaweed subalgebras

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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