Hunt for 3-Schur polynomials

Abstract

This paper describes our attempt to understand the recent success of Na Wang in constructing the 3-Schur polynomials, associated with the plane partitions. We provide a rather detailed review and try to figure out the new insights, which allowed to overcome the problems of the previous efforts. In result we provide a very simple definition of time-variables ${\mathbf{P}}_{i⩾j}$ and the cut-and-join operator ${\hat{W}}_2$, which generates the set of $3$-Schur functions. Some coefficients in ${\hat{W}}_2$ remain undefined and require more effort to be fixed.

References in corpus (3)

• On the complete perturbative solution of one-matrix models
• Superintegrability for ($\beta$-deformed) partition function hierarchies with $W$-representations
• Cauchy formula and the character ring

Cited by in corpus (11)

• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• 3-Schurs from explicit representation of Yangian $Y({\widehat{\mathfrak{gl}}}_1)$. Levels 1-5
• Simple Representations of BPS Algebras: the case of $Y({\widehat{\mathfrak{gl}}}_2)$
• Wall-Crossing Effects on Quiver BPS Algebras
• Macdonald polynomials for super-partitions
• On character expansion and Gaussian regularization of Itzykson-Zuber measure
• Integrability structures in string theory
• Supersymmetric polynomials and algebro-combinatorial duality
• Tunnels Under Geometries (or Instantons Know Their Algebras)
• Super-Hamiltonians for super-Macdonald polynomials
• Weyl Mutations in Quiver Yangians