The University of Illinois Algebra-Geometry-Combinatorics
Seminar |
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Giving a combinatorial explanation for the positivity of Schubert structure constants is a longstanding open problem. In this talk, which is based on joint work with Andy Hardt, we introduce an algebra on “chromatic words” which is homomorphic to the ring of back-stable quasisymmetric functions. By analyzing the preimage under this homomorphism of the product of two back-stable Schubert polynomials, we give a word-theoretic re-expression of the Schubert problem.
The seminar co-organizers are Ian Cavey, Andrew Hardt, David Keating, and Alexander Yong.