Abstract
In this paper we describe, in combinatorial terms, some matrices which arise as Laplacians connected to the three-dimensional Heisenberg Lie algebra. We pose the problem of finding the eigenvalues and eigenvectors of these matrices. We state a number of conjectures including the conjecture that all eigenvalues of these matrices are non-negative integers. We determine the eigenvalues and eigenvectors explicitly for an important subclass of these matrices.
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