Super-Schur polynomials for Affine Super Yangian Y( gl ̂ $$ \hat{\mathfrak{gl}} $$ 1|1)

Abstract

Abstract We explicitly construct cut-and-join operators and their eigenfunctions — the Super-Schur functions — for the case of the affine super-Yangian Y( gl ̂ $$ \hat{\mathfrak{gl}} $$ 1|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 , θ 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.

Keywords

• D-Branes
• Integrable Field Theories
• Quantum Groups