Pieri rules for Schur functions in superspace

The Schur functions in superspace $s_{\mathrm{\Lambda }}$ and ${\bar{s}}_{\mathrm{\Lambda }}$ are the limits $q=t=0$ and $q=t=\mathrm{\infty }$ respectively of the Macdonald polynomials in superspace. We prove Pieri rules for the bases $s_{\mathrm{\Lambda }}$ and $\bar s_{\Lambda}$ (which happen to be essentially dual). As a consequence, we derive the basic properties of these bases such as dualities, monomial expansions, and tableaux generating functions.