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 Pi⩾j and the cut-and-join operator Wˆ2, which generates the set of 3-Schur functions. Some coefficients in Wˆ2 remain undefined and require more effort to be fixed.

Topics & Concepts