2 results
A Hypergraph with Commuting Partial Laplacians
- Journal: Canadian Mathematical Bulletin / Volume 44 / Issue 4 / 01 December 2001
- Published online by Cambridge University Press: 20 November 2018, pp. 385-397
- Print publication: 01 December 2001
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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.
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Ramanujan Type Buildings
- Journal: Canadian Journal of Mathematics / Volume 52 / Issue 6 / 01 December 2000
- Published online by Cambridge University Press: 20 November 2018, pp. 1121-1148
- Print publication: 01 December 2000
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We will construct a finite union of finite quotients of the affine building of the group
$\text{G}{{\text{L}}_{3}}$ over the field of 
$p$-adic numbers 
${{\mathbb{Q}}_{p}}$. We will view this object as a hypergraph and estimate the spectrum of its underlying graph.
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