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On the linearity of lattices in affine buildings (Geometrietag)

On the linearity of lattices in affine buildings (Geometrietag)
Datum:18.11.2016 Ort:SR 0.014 (20.30)
Referent:Jean Lécureux
Zeit:11:30 - 12:30 Uhr

Abstract: Affine buildings are mostly useful because they admit nice actions by simple algebraic groups over local fields. However, there are some other constructions of 2-dimensional affine buildings, some of them with cocompact automorphism group.

After recalling the basic definitions and facts about affine buildings, I will explain the following theorem: a cocompact automorphism group of an $\tilde A_2$-building admits an infinite linear representation if and only if it is arithmetic. The proof uses ergodic techniques à la Margulis.

It is a joint work with Uri Bader and Pierre-Emmanuel Caprace.