Regarding a Representation-Theoretic Conjecture of Wigderson
Abstract
We show that there exists a family of irreducible representations Ri (of finite groups Gi) such that, for any constant t, the average of Ri over t uniformly random elements g1, ..., gt of Gi has operator norm 1 with probability approaching 1 as i limits to infinity. This settles a conjecture of Wigderson in the negative.
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