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arXiv · 1612.04133

Coxeter element and particle masses

Laura Brillon·Vadim Schechtman
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Abstract

Let $\mathfrak{g}$ be a simple Lie algebra of rank $r$ over $\mathbb{C}$, $\mathfrak{h} \subset \mathfrak{g}$ a Cartan subalgebra. We construct a family of $r$ commuting Hermitian operators acting on $\mathfrak{h}$ whose eigenvalues are equal to the coordinates of the eigenvectors of the Cartan matrix of $\mathfrak{g}$.

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Laura Brillon, Vadim Schechtman. 2016-12-13. Coxeter element and particle masses. https://doi.org/10.1007/s00029-016-0283-5

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