Explicit constructions of Ramanujan complexes of type Ad

Authors:
Alexander Lubotzky;Beth Samuels;Uzi Vishne
Affiliations:
Department of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel;Department of Mathematics, Yale University, 10 Hillhouse Avenue, New-Haven, CT;Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel and Department of Mathematics, Yale University, 10 Hillhouse Avenue, New-Haven, CT
Venue:
European Journal of Combinatorics - Special issue on combinatorics and representation theory
Year:
2005

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Abstract

In this paper we present for every d ≥ 2 and every local field F of positive characteristic, explicit constructions of Ramanujan complexes which are quotients of the Bruhat--Tits building Bd(F) associated with PGLd(F).