Geodesic
A Hypergraph with Commuting Partial Laplacians
Canadian mathematical bulletin, Tome 44 (2001) no. 4, pp. 385-397

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DOI

Let $F$ be a totally real number field and let $\text{G}{{\text{L}}_{n}}$ be the general linear group of rank $n$ over $F$ . Let $\mathfrak{p}$ be a prime ideal of $F$ and ${{F}_{\mathfrak{p}}}$ the completion of $F$ with respect to the valuation induced by $\mathfrak{p}$ . We will consider a finite quotient of the affine building of the group $\text{G}{{\text{L}}_{n}}$ over the field ${{F}_{\mathfrak{p}}}$ . We will view this object as a hypergraph and find a set of commuting operators whose sum will be the usual adjacency operator of the graph underlying the hypergraph.
DOI : 10.4153/CMB-2001-039-x
Mots-clés : 11F25, 20F32, Hecke operators, buildings 
Ballantine, Cristina M. A Hypergraph with Commuting Partial Laplacians. Canadian mathematical bulletin, Tome 44 (2001) no. 4, pp. 385-397. doi: 10.4153/CMB-2001-039-x
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     title = {A {Hypergraph} with {Commuting} {Partial} {Laplacians}},
     journal = {Canadian mathematical bulletin},
     pages = {385--397},
     year = {2001},
     volume = {44},
     number = {4},
     doi = {10.4153/CMB-2001-039-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-039-x/}
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