Explicit formulas are derived for the eigenvalues of Casimir operators D_{m,n} on SL(n,Z)-Maass forms in terms of Langlands parameters, with a graph-theoretic proof that recovers the known Laplacian case for m=2.
Eisenstein Series and the Trace Formula
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Explicit Formulas for the Casimir Eigenvalues of $SL(n,\mathbb{Z})$-Maass Forms
Explicit formulas are derived for the eigenvalues of Casimir operators D_{m,n} on SL(n,Z)-Maass forms in terms of Langlands parameters, with a graph-theoretic proof that recovers the known Laplacian case for m=2.