Frobenius seaweed subalgebras of type B_n and C_n have unbroken integer spectra under the adjoint action of a principal element, with symmetric multiplicities.
Joseph, The integrality of an adapted pair
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The unbroken spectrum of Frobenius seaweeds II: type-B and type-C
Frobenius seaweed subalgebras of type B_n and C_n have unbroken integer spectra under the adjoint action of a principal element, with symmetric multiplicities.