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Random Walks on Groups and Representation Theory

Final Report Summary - UB07 (Random Walks on Groups and Representation Theory)

The project enables us to develop a surprising link between random walk theory on groups and representation theory. Whereas this is a new theory and many questions and basic problems still remain a mystery, we were able to give a set of axioms to boundary theory and to associate with every group a pair of boundaries, and in particular a (smaller) group of symmetries, to be called 'the Weyl group' with representation theory which controls the representation theory of the ambient group. This is with an obvious similarity to the classical semi-simple theory.

Our project resulted in publishing various professional papers, as listed below.