Equivariant cohomology and intersection theory of affine Grassmannians for reductive groups

What the research examines

Establishes an explicit combinatorial formula for the torus-equivariant intersection cohomology of Schubert varieties in the affine Grassmannian, connecting geometric Satake equivalence with quantum Knizhnik-Zamolodchikov differential equations.

Why it may matter

Unifies modern geometric representation theory, quantum integrable systems, and algebraic topology.

What to examine carefully

Restricted to complex reductive algebraic groups and does not cover loop groups over fields of positive characteristic.

Try a small, reproducible follow-up

Compute Schubert classes and cup product multiplication tables in the cohomology ring of Grassmannian Gr(2, 4).

Questions to investigate

1. How does the localized equivariant GKM graph structure encode affine Weyl group reflections?
2. What connection exists between Schubert class intersection numbers and tensor product multiplicities of irreducible representations?

These are independently proposed educational investigations, not activities that the original research authors claim to have completed.

Publication & researcher information

Multi-author research may involve universities in several countries. Unverified institutions and contact addresses are not inferred from authors' names.

Primary sources