Burger, Marc
Iozzi, Alessandra
Monod, Nicolas
Equivariant embeddings of trees into hyperbolic spaces
International Mathematics Research Notices
10.1155/IMRN.2005.1331
22
1331-1369
We study isometric actions of tree automorphism groups on the infinite-dimensional hyperbolic spaces. On the one hand, we exhibit a general one-parameter family of such representations and analyse the corresponding equivariant embeddings of the trees, showing that they are convex-cocompact and asymptotically isometric. On the other hand, focusing on the case of sufficiently transitive groups of automorphisms of locally finite trees, we classify completely all irreducible representations by isometries of hyperbolic spaces. It turns out that in this case our one-parameter family exhausts all non-elementary representations.
2005