Date of Award
Doctor of Philosophy
Morwen B. Thistlethwaite
Conrad P. Plaut, James Conant, George Siopsis
We obtain explicit formulae for Lagrangian representations of the (p, q, r)-triangle group into the group of direct isometries of the complex hyperbolic plane in the case where p=q=r. Numerically approximated matrix generators of representations of the (p, p, p)-triangle group are obtained using a special basis. The numerical approximations are then used to guess the exact generators by a process utilizing the LLL algorithm. The matrices are proved rigorously to generate Lagrangian representations of the (p, p, p)-triangle group and are applied to the problem of deciding whether or not an interval contains representations of the (p, p, p)-triangle group which are not discrete.
Lewis, Paul Wayne Jr., "Lagrangian Representations of (p, p, p)-triangle Groups. " PhD diss., University of Tennessee, 2011.