Pieri rules for Schur functions in superspace

Abstract

The Schur functions in superspace $s_{\Lambda }$ and ${\bar{s}}_{\Lambda }$ are the limits $q=t=0$ and $q=t=\infty$ respectively of the Macdonald polynomials in superspace. We prove Pieri rules for the bases $s_{\Lambda }$ 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.

43 pages