Generic spectrum of the weighted Laplacian operator on Cayley graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866913376449331200 |
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| author | Coletti, Cristian F. de Lima, Lucas R. de Oliveira, Diego S. Marrocos, Marcus A. M. |
| author_facet | Coletti, Cristian F. de Lima, Lucas R. de Oliveira, Diego S. Marrocos, Marcus A. M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_07908 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Generic spectrum of the weighted Laplacian operator on Cayley graphs Coletti, Cristian F. de Lima, Lucas R. de Oliveira, Diego S. Marrocos, Marcus A. M. Spectral Theory Mathematical Physics Combinatorics 05C50, 47A75, 47A55 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. |
| title | Generic spectrum of the weighted Laplacian operator on Cayley graphs |
| topic | Spectral Theory Mathematical Physics Combinatorics 05C50, 47A75, 47A55 |
| url | https://arxiv.org/abs/2009.07908 |