Notes on Schubert classes of a loop group

Abstract

In these notes, we survey the homology of the loop group Omega(K) of a compact group K, also known as the affine Grassmannian of a complex loop group. Using the Bott picture of H_*(Omega(K)), the homology algebra or Pontryagin ring, we obtain two new results: A. Factorization of affine Schubert homology classes. B. Definition of affine Schubert polynomials representing the affine Schubert homology classes in all types, in terms similar to ordinary Schubert polynomials.

Cited by in corpus (2)

• Generating varieties for affine Grassmannians
• Affine symmetries of the equivariant quantum cohomology ring of rational homogeneous spaces