| Details: |
A reflection group is a subgroup of orthogonal or unitary group generated by (possibly complex) reflections. In the first part of the talk we shall describe nice Coxeter-type generators and relations for many interesting reflection groups.
In the second part we shall focus on one particular reflection group R in U(13,1). This group R naturally acts on the the unit ball B in the complex 13 dimensional vector space. Let B_reg be the subset of B on which R acts freely. We shall describe generators and relations for the fundamental group G of (B_reg/R). The generators and relations for R and G are similar to generators and relations known for a group closely related to the monster simple group. We shall discuss a precise conjecture relating G and the monster due to Daniel Allcock.
We will not assume familiarity with the theory of complex or hyperbolic reflection groups or the monster. |