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A Hypergraph with Commuting Partial Laplacians

Published online by Cambridge University Press:  20 November 2018

Cristina M. Ballantine
Cristina M. Ballantine*
Affiliation:
Department of Mathematics University of Toronto Toronto, Ontario M5A 3G3 Department of Mathematics Bowdoin College Brunswick, Maine 04011 U.S.A., email: cballant@bowdoin.edu
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Abstract

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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.

Keywords

11F2520F32Hecke operatorsbuildings
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 4 , 01 December 2001 , pp. 385 - 397
Copyright
Copyright © Canadian Mathematical Society 2001

References

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