Two-sided hyperbolic Kazhdan-Lusztig cells

Here are pictures of Kazhdan-Lusztig cells for some hyperbolic planar Coxeter groups. The pictures were generated by kludging together different pieces of software:

• Automatic group computations, like getting a list of all words in a Coxeter group up to a given length, or finding canonical reduced expressions for group elements, were done using Derek Holt's program kbmag2.
• Computation of Kazhdan-Lusztig polynomials was done by a hacked version of Fokko du Cloux's program coxeter.
• The hyperbolic Postscript routines were written by Bill Casselman.
• Finally, everything was glued together using Perl.

The files

Each group can be downloaded in gzipped Postscript, Postscript, or PDF. The Postscript files look better at different sizes, but they are rather large. You can get the whole mess as a gzipped tarfile of Postscript files.

Triangle groups

The notation p q r means the triangle group generated by reflections through the sides of a hyperbolic triangle with angles (Pi/p, Pi/q, Pi/r).

• 2 3 7 ps, ps.gz, pdf
• 2 3 8 ps, ps.gz, pdf
• 2 3 9 ps, ps.gz, pdf
• 2 3 11 ps, ps.gz, pdf
• 2 3 infinity (the modular group PSL(2,Z)) ps, ps.gz, pdf
• 2 4 5 ps, ps.gz, pdf
• 2 4 6 ps, ps.gz, pdf
• 2 5 5 ps, ps.gz, pdf
• 2 6 6 ps, ps.gz, pdf
• 2 infinity infinity ps, ps.gz, pdf
• 4 4 4 ps, ps.gz, pdf

Quadrilateral groups

Here the notation p q r s means the group generated by reflections through the sides of a hyperbolic quadrilateral with angles (Pi/p, Pi/q, Pi/r, Pi/s).

• 2 2 2 3 ps, ps.gz, pdf
• 2 2 2 4 ps, ps.gz, pdf