Abstract

. Let G be a compact group acting in a real vector space V. We obtain a number of inequalities relating the L∞ norm of a matrix element of the representation of G with its L 2k norm for a positive integer k. As an application, we obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial over the unit sphere and for the assignment problem of degree d, a hard problem of combinatorial optimization generalizing the quadratic assignment problem.