Speaker

:

Dr. Tathagatha Basak

Subject Area

:

Mathematics

Venue

:

Lecture Hall - I, Dept of Mathematics

Time

:

11 am

Date  

:

August 21, 2009 (Friday)

Title

:

A complex hyperbolic reflection group and the bimonster

Let R be the reflection group of the complex leech lattice plus a hyperbolic cell. Let D be the incidence graph of the projective plane over the finite field with 3 elements. Let A(D) be the Artin group of D: generators of A(D) correspond to vertices of D. Two generators braid if there is an edge between them, otherwise they commute.

It is surprising that both the bimonster and the reflection group R are quotients of A(D) when the generators are mapped to elements of order 2 and 3 respectively. A conjecture by Daniel Allcock seeks to explain this connection between R and the bimonster. We shall try to explain some of the evidences for the conjecture so far.

We shall see that D behaves like the Coxeter-Dynkin diagram for the reflection group R. This imprecise analogy with Weyl groups actually makes our proofs work. There is a parallel story for a quaternionic hyperbolic reflection group where the analogies repeat