Marked length spectrum on the finite set of elements determines the irreducible representation in the isometry group of rank one symmetric space of noncompact type (Q2752839)

In this paper, it is shown that the space of irreducible representations from a finitely presented group into the group of isometries of a rank one symmetric space of noncompact type (other than the Cayley hyperbolic plane) embeds into \({\mathbb R}^n\) for some \(n\), where the coordinates are the translation lengths of isometries in the representation. The proof relies on the following result by the author [Topology 40, No. 6, 1295-1323 (2001; Zbl 0997.53034)]: Let \(\rho,\phi\) be non-elementary irreducible representations from a group \(G\) into Iso\((X)\), where \(X\) is a rank one symmetric space of noncompact type. If they have the same marked length spectrum, then they are conjugate.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00035].