Regarding a Representation-Theoretic Conjecture of Wigderson

Details Regarding a Representation-Theoretic Conjecture of Wigderson Regarding a Representation-Theoretic Conjecture of Wigderson

2010-09-21

arxiv.org/abs/1009.4136v1

Mathematics

Group Theory

Scientific paper

We show that there exists a family of irreducible representations R_i (of
finite groups G_i) such that, for any constant t, the average of R_i over t
uniformly random elements g_1, ..., g_t of G_i 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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