Ramanujan bigraphs associated with SU(3) over a p-adic field
Representation Theory
2010-05-20 v1 Combinatorics
Abstract
We use the representation theory of the quasisplit form G of SU(3) over a p-adic field to investigate whether certain quotients of the Bruhat--Tits tree associated to this form are Ramanujan bigraphs. We show that a quotient of the tree associated with G (which is a biregular bigraph) is Ramanujan if and only if G satisfies a Ramanujan type conjecture. This result is analogous to the seminal case of PGL(2) considered by Lubotzky-Phillips-Sarnak. As a consequence, the classification by Rogawski of the automorphic spectrum of U(3) implies the existence of certain infinite families of Ramanujan bigraphs.
Cite
@article{arxiv.1005.3504,
title = {Ramanujan bigraphs associated with SU(3) over a p-adic field},
author = {Cristina Ballantine and Dan Ciubotaru},
journal= {arXiv preprint arXiv:1005.3504},
year = {2010}
}
Comments
16 pages