Notes on Schubert classes of a loop group
Representation Theory
2007-05-28 v1 K-Theory and Homology
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.
Cite
@article{arxiv.0705.3826,
title = {Notes on Schubert classes of a loop group},
author = {Peter Magyar},
journal= {arXiv preprint arXiv:0705.3826},
year = {2007}
}