A Schubert curve

Here is a Schubert curve (see this paper or a new, soon-to-be-completed paper for details):

The top curve, S, is a Schubert curve -- an intersection of three Schubert varieties in the Grassmannian, defined using what are called "osculating flags". The codimensions are chosen to leave one "degree of freedom", in order to guarantee that the intersection is a curve.

The bottom curve is an ordinary RP^1, marked with three partitions (alpha, beta and gamma), corresponding to the three Schubert varieties.

The reason this is interesting is that the Schubert curve is a covering space of the RP^1! The preimages of zero and infinity correspond to certain "semistandard Young tableaux" (the grids of numbers shown), and following the loop of the Schubert curve corresponds to moving the "x" square of the tableau according to a combinatorial algorithm.

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