Hall 123

On Symmetric functions

S.Velmurugun

IMSc, Chennai

Let $\{u_n\}$ be a sequence of symmetric functions, where $u_n$ is homogeneous of degree $n$. We know of many sequences $\{u_n\}$ which generate for the algebra of symmetric functions. For instance, complete, elementary, and power sum symmetric functions. Are there more? Obviously yes. In fact, there are a many!

D G Mead (1993) observed that if $u_n$ is any monomial symmetric function of degree $n$ for each $n\geq 0$, then $\{u_n\}$ is a generating sequence. We examine when sequences taken from other familiar families of symmetric function (Schur, skew-Schur, skew-monomial, skew-complete, Hall-Littlewood, Macdonald, etc.) are generators.