A Haagerup inequality for A1 x A1 and A2 buildings

Authors

Jacqueline Ramagge, University of NewcastleFollow
Guyan Robertson, University of Newcastle
Tim Steger, Universita degli Studi di Sassari

RIS ID

17633

Publication Details

Ramagge, J., Robertson, A. G. & Steger, T. (1998). A Haagerup inequality for A₁ x A₁ and A₂ buildings. Geometric and Functional Analysis, 8, 702-731.

Abstract

Haagerup's inequality for convolvers on free groups may be interpreted as a result on A₁ buildings, i.e. trees. Here are proved analogous inequalities for discrete groups acting freely on the vertices of A₁ x A₁ and A₂ buildings. The results apply in particular to groups of typerotating automorphisms acting simply transitively on the vertices of such buildings. These results provide the first examples of higher rank groups with property (RD).