Some special discrete groups of linear transformations
Wulf Rossmann (Ottawa)
Examples of the groups I have in mind are the following. A Weyl group
acting on a space of characters of its Lie group by coherent continuation.
A Weyl group acting on the homology of the fixed point set of a unipotent
element on the flag manifold by Springer's representation. The modular
group SL(2,Z) acting on a space of theta functions in one variable. More
generally, the symplectic group Sp(2g,Z) acting on a space of theta
functions in any number of variables, which turns out to be a finite
metaplectic group Mp(2g,Z/nZ). At first sight these examples may not
appear to have much in common, but all of them can be shown to arise in
the same way, by the same geometric construction. It is the purpose of
the talk to explain this construction.
Return to conference