JournalsjstVol. 7, No. 3pp. 907–937

Quantum Cayley graphs for free groups

  • Robert Carlson

    University of Colorado at Colorado Springs, USA
Quantum Cayley graphs for free groups cover

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Abstract

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

Cite this article

Robert Carlson, Quantum Cayley graphs for free groups. J. Spectr. Theory 7 (2017), no. 3, pp. 907–937

DOI 10.4171/JST/181