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An answer to Kac's question on Coxeter exponents Liu, Zhengwei


In the ADE quiver theory, there is a correspondence between the eigenvalues of the Coxeter element and the eigenvalues of the adjacency matrix, captured by the Coxeter exponents. We formalize related notations and prove such a correspondence for a more general case: this includes the quiver of any module of any semisimple Lie algebra g at any level l. We answer a question posed by Victor Kac in 1994 and a recent comment by Terry Gannon in 2017.

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