A partial ordering of CS m defined by the generalized matrix functions

Abstract

We present a description of a partial ordering of the complex full symmetric group algebra, CS m , via generalized matrix functions, d f ( A), defined on the set of all m × m complex matrices A. We show that for f:S m → C, if d f ( A) = 0 for all positive semidefinite Hermitian matrices A, then f = 0. Thus we can build up a partial ordering for CS m .