Cut-and-join operators and Macdonald polynomials from the 3-Schur functions

Abstract

We demonstrate in some detail how Macdonald polynomials emerge from the recently introduced 3-Schur functions when the plane-partition vector time-variables are projected onto the ordinary scalar times under non-vanishing angles, which depend on $q$ and $t$. We also explain how the cut-and-join operators smoothly interpolate between different cases. Most of consideration is restricted to level two.

21 pages

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Cited by in corpus (6)

• A slow review of the AGT correspondence
• Hunt for 3-Schur polynomials
• 3-Schurs from explicit representation of Yangian $Y({\widehat{\mathfrak{gl}}}_1)$. Levels 1-5
• On Hamiltonians for Kerov functions
• On generalized Macdonald polynomials
• Equating Schur Functions