Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{g}\mathfrak{l}}}_{1\mathrm{\mid }1})$

We explicitly construct cut-and-join operators and their eigenfunctions – the Super-Schur functions – for the case of the affine super-Yangian $\mathsf{Y}({\widehat{\mathfrak{g}\mathfrak{l}}}_{1\mathrm{\mid }1})$. This is the simplest non-trivial (semi-Fock) representation, where eigenfunctions are labeled by the superanalogue of 2d Young diagrams, and depend on the supertime variables $(p_k,{\theta }_k)$. The action of other generators on diagrams is described by the analogue of the Pieri rule. As well we present generalizations of the hook formula for the measure on super-Young diagrams and of the Cauchy formula. Also a discussion of string theory origins for these relations is provided.