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.
| Identifer | oai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_graddiss-2304 |
| Date | 01 December 2011 |
| Creators | Lewis, Paul Wayne, Jr. |
| Publisher | Trace: Tennessee Research and Creative Exchange |
| Source Sets | University of Tennessee Libraries |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Doctoral Dissertations |
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