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.
acameron@bloomu.edu
Vincent E. Coll Jr.
Department of Mathematics, Lehigh University, Bethlehem, U.S.A.
vec208@lehigh.edu
Matthew Hyatt
FactSet Research Systems, New York, U.S.A.
matthewdhyatt@gmail.com
Colton Magnant
UPS of America, Atlanta, U.S.A.
cmagnant@ups.com
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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