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Matrix coefficients of finite groups

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Let G be a finite group, and let f be a d-dimensional unitary representation of G. Let v be a d-dimensional complex unit vector. We show that there is another unit vector w such that the inner product of f(g) v and w is O((log d)-1/2), uniformly for all g in G. Geometrically (a real version of this) states that ``finite transitive subsets of the d-dimensional sphere have width O((log d)-1/2)”, or in other words they are “almost flat”.

This talk is part of the Discrete Analysis Seminar series.

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