Elliptic triangle groups in PU(2, 1), Lagrangian triples and momentum maps
نویسنده
چکیده
We determine the possible eigenvalues of elliptic matrices A,B, C in PU(2, 1) satisfying ABC = 1. This is done by describing geometrically the image of a certain momentum map for the (non-compact) group action of PU(2, 1) by conjugation on C1 × C2 where C1 and C2 are fixed elliptic conjugacy classes in PU(2, 1). Surprisingly, this image is not always convex, rather it is the union of one, two or three convex polygons in T 2/S2. The main motivation was to analyse elliptic triangle groups in PU(2, 1) such as Mostow’s lattices.
منابع مشابه
Ideal triangle groups , dented tori , and numerical analysis By Richard
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