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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_2001_039_x,
     author = {Ballantine, Cristina M.},
     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/}
}
TY  - JOUR
AU  - Ballantine, Cristina M.
TI  - A Hypergraph with Commuting Partial Laplacians
JO  - Canadian mathematical bulletin
PY  - 2001
SP  - 385
EP  - 397
VL  - 44
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-039-x/
DO  - 10.4153/CMB-2001-039-x
ID  - 10_4153_CMB_2001_039_x
ER  - 
%0 Journal Article
%A Ballantine, Cristina M.
%T A Hypergraph with Commuting Partial Laplacians
%J Canadian mathematical bulletin
%D 2001
%P 385-397
%V 44
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-039-x/
%R 10.4153/CMB-2001-039-x
%F 10_4153_CMB_2001_039_x

[1] [1] Ballantine, C., Hypergraphs and Automorphic Forms. PhD Thesis, Toronto, 1998. Google Scholar

[2] [2] Bollobas, B.. Extremal Graph Theory. LMS Monographs, Academic Press 1978. Google Scholar

[3] [3] Borel, A.. Linear algebraic groups. Springer-Verlag 1991. Google Scholar

[4] [4] Borel, A., Some finiteness properties of adele groups over number fields. Inst.Hautes Études Sci. Publ. Math. 16 (1963), 5–30. Google Scholar

[5] [5] Brown, K. S.. Buildings. Springer-Verlag, New York, 1989. Google Scholar

[6] [6] Cartier, P.. Representations of p-adic groups: A survey. Automorphic forms, representations, and L-functions, Proc. Sympos. Pure Math. 33, Part I (eds. A. Borel and W. Casselman), Amer.Math. Soc., Providence, R.I. 1979, 111–155. Google Scholar

[7] [7] Lubotzky, A.. Discrete groups, expanding graphs and invariant measures. Progress in Math. 125, Birkhauser Verlag, 1994. Google Scholar

[8] [8] Rogawski, J. D.. Automorphic representations of the unitary group in three variables. Ann. of Math. Studies 123, Princeton Univ. Press, Princeton, New Jersey, 1990. Google Scholar

[9] [9] Selberg, A.. On discontinuous groups in higher-dimensional symmetric spaces. Contributions to Function Theory, International Colloquia on Function Theory, Bombay, 1960, 147–164, Tata Institute of Fundamental Research, Bombay, 1960. Google Scholar

[10] [10] Tits, J.. Reductive groups over local fields. Automorphic forms, representations, and L-functions, Proc. Sympos. Pure Math. 33, Part I (eds. A. Borel and W. Casselman), Amer. Math. Soc., Providence, R.I. 1979, 29–69. Google Scholar

Cité par Sources :