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, GromovWitten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian. We introduce operators on decompositions of elements in the typeA 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 kSchur function, consequently proving that a subclass of 3point GromovWitten 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 byproduct 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
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Speaker: Anne Schilling
Institution: UC Davis
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