3 problems

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Valette's rapid decay conjecture for uniform lattices in semisimple Lie groups
Valette's conjecture. Property (RD) holds for uniform lattices in $\operatorname{SL}_d(\operatorname{\mathbb{R}})$ ; more generally, it holds for uniform lattices in any semisimple…
Conjectureopengeometric-group-theory property-rd semisimple-lie-groupsarXiv posted 2 days ago
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Optimal Haagerup inequality constant for affine $\widetilde{A}_2$ buildings
Optimal-constant conjecture. The optimal value of $p(m,n)$ in the $\widetilde{A}_2$ case is
Conjectureopenaffine-buildings haagerup-inequality property-rdarXiv posted 2 days ago
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Valette's conjecture on property (RD) for cocompact lattices
Let $\Lambda$ be a cocompact lattice in a simple algebraic group over a local field. Valette's conjecture. Every such lattice $\Lambda$ has property (RD). Thus a cocompact lattice…
Conjectureopenlattices locally-compact-groups property-rdarXiv posted 2 days ago

Valette's rapid decay conjecture for uniform lattices in semisimple Lie groups