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The A.B.C.Ds of Schubert calculus

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arxiv 1906.03646 v1 pith:AOKMUXX7 submitted 2019-06-09 math.CO math.AG

Colleen Robichaux , Harshit Yadav , Alexander Yong This is my paper · ORCID
classification math.COmath.AG
keywords calculusschubertatiyah-bottbergeron-fbilley-mbuch-vcoefficientscohomology
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We collect Atiyah-Bott Combinatorial Dreams (A.B.C.Ds) in Schubert calculus. One result relates equivariant structure coefficients for two isotropic flag manifolds, with consequences to the thesis of C. Monical. We contextualize using work of N. Bergeron-F. Sottile, S. Billey-M. Haiman, P. Pragacz, and T. Ikeda-L. Mihalcea-I. Naruse. The relation complements a theorem of A. Kresch-H. Tamvakis in quantum cohomology. Results of A. Buch-V. Ravikumar rule out a similar correspondence in K-theory.

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  1. Equivariant cohomology, Schubert calculus, and edge labeled tableaux

    math.CO 2019-08 conditional novelty 7.0 of 10

    A new shifted analogue of edge labeled tableaux is defined and conjecturally gives a Littlewood-Richardson rule for the D. Anderson-W. Fulton ring in equivariant Schubert calculus.

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