2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63035Let G be a compact group acting in a real vector space V. We obtain a number of inequalities relating the L^infinity norm of a matrix element of the representation of G with its L^p norm for p<infinity. We apply our results to obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial over the unit sphere (in which case G is the orthogonal group) and for the multidimensional assignment problem, a hard problem of combinatorial optimization (in which case G is the symmetric group).Optimization and ControlCombinatoricsRepresentation Theory68W25; 68R05; 90C30; 90C27; 20C15text