alexa Index of parabolic and seaweed subalgebras of son
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Alexander Dvorsky

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The index of a Lie algebra r is defined as minw∈r∗dimrw, 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 ind q<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.

This article was published in Linear Algebra and its Applications and referenced in Journal of Generalized Lie Theory and Applications

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