The A.B.C.Ds Of Schubert Calculus

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 and F. Sottile, of S. Billey and M. Haiman, of P. Pragacz, and of T. Ikeda, L. Mihalcea, and I. Naruse. The relation complements a theorem of A. Kresch and H. Tamvakis in quantum cohomology. Results of A. Buch and V. Ravikumar rule out a similar correspondence in K-theory.