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Journal of Lie Theory 33 (2023), No. 2, 609--639
Copyright Heldermann Verlag 2023

The Unbroken Spectra of Frobenius Seaweed Algebras

Alex Cameron
Department of Mathematics, Bloomsburg University, Bloomsburg, U.S.A.

Vincent E. Coll Jr.
Department of Mathematics, Lehigh University, Bethlehem, U.S.A.

Matthew Hyatt
FactSet Research Systems, New York, U.S.A.

Colton Magnant
UPS of America, Atlanta, U.S.A.

We show that if g is a Frobenius seaweed, then the spectrum of the adjoint of a principal element consists of an unbroken set of integers whose multiplicities have a symmetric distribution. Our methods are combinatorial.

Keywords: Frobenius Lie algebra, seaweed, biparabolic, principal element, Dynkin diagram, spectrum, regular functional, Weyl group.

MSC: 17B20, 05E15.

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