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Hunt for 3-Schur polynomials
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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 ${\bf P}_{i\geqslant j}$ 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.
Forward citations
Cited by 2 Pith papers
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Super-Hamiltonians for super-Macdonald polynomials
Explicit vertex-operator super-Hamiltonians are conjectured whose eigenfunctions are the super-Macdonald polynomials of earlier work.
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Weyl Mutations in Quiver Yangians
Weyl group reflections act as Seiberg-like dualities on A_n quiver gauge theories, mapping stability chambers to each other while conjecturally leaving the quiver Yangian Y(sl_{n+1}) invariant.
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