Regarding a Representation-Theoretic Conjecture of Wigderson
Group Theory
2010-09-22 v1 Computational Complexity
Representation Theory
Abstract
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.
Cite
@article{arxiv.1009.4136,
title = {Regarding a Representation-Theoretic Conjecture of Wigderson},
author = {Cristopher Moore and Alexander Russell},
journal= {arXiv preprint arXiv:1009.4136},
year = {2010}
}