The direct sum morphism in (equivariant) Schubert calculus

Direct sum of subspaces defines a map on Grassmannians, which, after taking an appropriate limit, leads to a product-like structure on the infinite Grassmannian.  The corresponding cohomology pullback coincides with a famous co-product on the ring of symmetric functions.  I’ll describe torus-equivariant extensions of this setup, along with positivity results for structure constants, and some open questions.  This story partially extends work by Thomas-Yong, Knutson-Lederer, and Lam-Lee-Shimozono, and connects to joint work with W. Fulton.  (No special knowledge of Schubert calculus -- equivariant or not -- will be assumed.)