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arXiv · 1005.3504

Ramanujan bigraphs associated with SU(3) over a p-adic field

Cristina Ballantine·Dan Ciubotaru
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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.

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Cristina Ballantine, Dan Ciubotaru. 2010-05-19. Ramanujan bigraphs associated with SU(3) over a p-adic field. https://arxiv.org/abs/1005.3504

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