Abstract: What do Fubini words and Affine Springer fibers have in common? They both arise amid a new connection between the Rational Shuffle Theorem and the Delta Theorem via a skewing operator.  We present this new formula, and explore some combinatorial and geometric interpretations. This provides the first geometric interpretation of the Delta polynomials, via a generalization of Hikita’s work on affine Springer fibers for the Shuffle theorem specialization, using partial affine flag varieties. Our work can also be interpreted as providing a new combinatorial proof of the Rise Delta theorem, starting with the Rational Shuffle formula.

 

This is joint work with Sean Griffin and Eugene Gorsky.

 

Host: Martha Precup