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arXiv · 1302.5598

A Haagerup Inequality for $\tA_1\times\tA_1$ and $\tA_2$ Buildings

Jacqui Ramagge·Guyan Robertson·Tim Steger
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Abstract

Haagerup's inequality for convolvers on free groups may be interpreted as a result on $\tA_1$ buildings, i.e. trees. Here are proved analogous inequalities for discrete groups acting freely on the vertices of $\tA_1\times\tA_1$ and $\tA_2$ buildings. The results apply in particular to groups of type-rotating automorphisms acting simply transitively on the vertices of such buildings. These results provide the first examples of higher rank groups with property (RD).

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Jacqui Ramagge, Guyan Robertson, Tim Steger. 2013-02-22. A Haagerup Inequality for $\tA_1\times\tA_1$ and $\tA_2$ Buildings. https://arxiv.org/abs/1302.5598

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