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Ramanujan Complexes of Type $\tilde{A_d}$

Alex Lubotzky·Beth Samuels·Uzi Vishne
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Abstract

We define and construct Ramanujan complexes. These are simplicial complexes which are higher dimensional analogues of Ramanujan graphs. They are obtained as quotients of the buildings of type $\tilde{A}_{d-1}$ associated with $\operatorname{PGL}_d(F)$ where $F$ is a local field of positive characteristic.

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BibTeXRIS

Alex Lubotzky, Beth Samuels, Uzi Vishne. 2005-01-05. Ramanujan Complexes of Type $\tilde{A_d}$. https://arxiv.org/abs/math/0406208

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