Quantum Cayley graphs for free groups (Q1674007)

Summary: Dierential operators \(\Delta + q\) are considered on metric Cayley graphs of the nitely generated free groups \(\mathbb F_M\). The function \(q\) and the graph edge lengths may vary with the \(M\) edge types. Using novel methods, a set of \(M\) multipliers \(\mu_m(\lambda)\) depending on the spectral parameter is found. These multipliers are used to construct the resolvent and characterize the spectrum.