Ramanujan Complexes of Type $\tilde{A_d}$

Alex Lubotzky; Beth Samuels; Uzi Vishne

arxiv: math/0406208 · v2 · submitted 2004-06-10 · 🧮 math.RT · math.GR

Ramanujan Complexes of Type tilde{A_d}

Alex Lubotzky , Beth Samuels , Uzi Vishne This is my paper

classification 🧮 math.RT math.GR

keywords complexesramanujantildetypeanaloguesassociatedbuildingscharacteristic

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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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Ramanujan Complexes of Type tilde{A_d}

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