Return to Colloquia & Seminar listing
``Coxeter Diagram'' for a complex hyperbolic reflection group and the bimonster
Algebra & Discrete Mathematics| Speaker: | Tathagata Basak, UC Berkeley |
| Location: | 1147 MSB |
| Start time: | Thu, Feb 16 2006, 12:10PM |
Description
Let D be the incidence graph of the projective plane over the finite
field with 3 elements. Conway, Ivanov et.al. gave a remarkably simple
presentation of the wreath product of the monster with Z/2 on the Coxeter
diagram D.
Let L be the direct sum of the complex Leech lattice and a hyperbolic
cell.
We will describe 26 complex reflections generating the automorphism group
of L that form the same Coxeter diagram D under braiding and commuting
relations.
We'll see that our example has surprising analogies with the theory of
Weyl group that make our proofs work. D acts as the Coxeter-Dynkin diagram
for the reflection group of L. There is a parallel story for the
quaternionic Leech lattice where the surprises repeat.