A Family of Schubert Structure Coefficients

Motivated by the Schubert-class expansion of the permutahedral variety in the cohomology of the complete flag variety, I will describe a family of Schubert multiplication coefficients that admit a combinatorial computation. The method combines Knutson’s descent cycling with Bergeron–Sottile operators, building on joint work with Philippe Nadeau and Hunter Spink centering around geometric aspects of quasisymmetric polynomials. As an application, I will resolve a Schubert-positivity question posed by Karp and Precup, arising from their study of Springer-fiber components that are Richardson varieties.

For information about the Richard P. Stanley Seminar in Combinatorics, visit… https://math.mit.edu/combin/