Resumen de Elliptic triangle groups in , Lagrangian triples and momentum maps

Julien Paupert

• We determine the possible eigenvalues of elliptic matrices in satisfying . This is done by describing geometrically the image of a group-valued momentum map for the (non-compact) group action of by conjugation on where and are fixed elliptic conjugacy classes in . Contrary to the compact case, this image is not always convex; rather it is the union of one, two or three convex polygons in . The main motivation was to analyze elliptic triangle groups in such as Mostow¿s lattices