Generic spectrum of the weighted Laplacian operator on Cayley graphs
Abstract
In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on left-invariant Cayley graphs endowed with an invariant metric, and we give some criteria for generically irreducible eigenspaces. Additionally, we introduce an operator that is comparable to the Laplacian and show that the same criterion holds.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.07908
- arXiv:
- arXiv:2009.07908
- Bibcode:
- 2020arXiv200907908C
- Keywords:
-
- Mathematics - Spectral Theory;
- Mathematical Physics;
- Mathematics - Combinatorics;
- 05C50;
- 47A75;
- 47A55
- E-Print:
- 18 pages, 2 figures