Some special discrete groups of linear transformations
 Wulf Rossmann (Ottawa)

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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.

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