Algebras of symmetric holomorphic functions on
l_{p}

We study the Banach algebra of uniformly continuous holomorphic
symmetric functions on the unit
ball of l_{p},
investigating in particular the
spectrum of such algebras. To do so, we examine the algebra of symmetric
polynomials on l_{p}-spaces as well as finitely
generated symmetric algebras of holomorphic functions. Such
symmetric polynomials determine the points in
l_{p} up to a permutation.