The m/n Pieri rule

The Pieri rule is an important theorem which explains how the operators e_k of multiplication by elementary symmetric functions act in the basis of Schur functions s_lambda. In this paper, for any rational number m/n, we study the relationship between the rational version e_k^{m/n} of the operators (given by the elliptic Hall algebra) and the "rational" version s_lambda^{m/n} of the basis (given by the Maulik-Okounkov stable basis construction)