  In the Hopf algebra of symmetric functions, Sym, the basis of Schur functions
is distinguished since every Schur function is isomorphic to an irreducible
character of a symmetric group under the Frobenius characteristic map. In this
note we show that in the Hopf algebra of noncommutative symmetric functions,
Nsym, of which Sym is a quotient, the recently discovered basis of
noncommutative Schur functions exhibits that every noncommutative Schur
function is isomorphic to a noncommutative irreducible character of a symmetric
group when working in noncommutative character theory. We simultaneously show
that a second basis of Nsym consisting of Young noncommutative Schur functions
also satisfies that every element is isomorphic to a noncommutative irreducible
character of a symmetric group.
