Papers › Combinatorics of Vogan diagrams for almost-Kähler manifolds
Combinatorics of Vogan diagrams for almost-Kähler manifolds
Alice Gatti
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Let G be a non-compact classical semisimple Lie group and let G/V be the adjoint orbit with respect to a fixed element in G. These manifolds can be equipped with an almost-K\"ahler structure and we provide explicit formulae for the existence of special almost-complex structures on G/V purely in terms of the combinatorics of the associated Vogan diagram. The formulae are given separately for Lie groups whose Lie algebras are of type A_ℓ, B_ℓ, C_ℓ, D_ℓ, where ℓ denotes the rank of the Lie algebra.
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