  The group of simplicial automorphisms of a Tits-Kac-Moody ininite building of
thickness q associated to a cocompact reflexion group with fundamental domain a
simplex, is Kazhdan for q sufficiently large. Thus we obtain families of new
Kazhdan groups: two in dimension 3 and one in dimension 4. The proof uses
continuos cohomology, in particular a lemma of Borel-Wallach, and Garland's
vanishing method.
