For a Toda-Weyl Lagrangian based on a Weyl group element sigma, the classical masses equal the absolute values of the pairings of the eigenvector Lambda+ with one representative from each sigma-orbit of roots.
Dorey, Root systems and purely elastic S-matrices, Nucl
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The Toda-Weyl mass spectrum
For a Toda-Weyl Lagrangian based on a Weyl group element sigma, the classical masses equal the absolute values of the pairings of the eigenvector Lambda+ with one representative from each sigma-orbit of roots.