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Unitary representations of reflection groups and their deformations.

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NPCW04 - Approximation, deformation, quasification

The first two parts of my talk will consist of independent surveys of exciting theories.
1. I will discuss the theory of ”boundary representations”, which consists of the study of a class of unitary representations arising naturally in geometric group theory.
2. I will describe the deformation theory of a right-angled Coxeter group W, known as the Iwahori-Hecke algebra H.
Later I will combine the two and focus on the boundary representation of W and explain how it deforms into a representation of H.
If time permits, I will relate the above to the boundary representations of groups which act on hyperbolic buildings.

Based on a joint work with Jan Dymara.

This talk is part of the Isaac Newton Institute Seminar Series series.

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