|Date: Friday, September 19, 2014
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Crystal approach to affine Schubert calculus
Abstract: We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian. We introduce operators on decompositions of elements in the type-A affine Weyl group and produce a crystal reflecting the internal structure of the generalized Young modules whose Frobenius image is represented by stable Schubert polynomials. We apply the crystal framework to products of a Schur function with a k-Schur function, consequently proving that a subclass of 3-point Gromov-Witten invariants of complete flag varieties for C^n enumerate the highest weight elements under these operators. Included in this class are the Schubert structure constants in the (quantum) product of a Schubert polynomial with a Schur function s_\lambda for all |\lambda^\vee|< n. Another by-product gives a highest weight formulation for various fusion coefficients of the Verlinde algebra and for the Schubert decomposition of certain positroid classes.
This is joint work with Jennifer Morse, see http://arxiv.org/abs/1408.0320
Speaker: Anne Schilling
Institution: UC Davis