Ktheory Schubert calculus of the affine Grassmannian
Abstract
We construct the Schubert basis of the torusequivariant Khomology of the affine Grassmannian of a simple algebraic group G, using the Ktheoretic NilHecke ring of Kostant and Kumar. This is the Ktheoretic analogue of a construction of Peterson in equivariant homology. For the case G = SL_n, the Khomology of the affine Grassmannian is identified with a subHopf algebra of the ring of symmetric functions. The Schubert basis is represented by inhomogeneous symmetric functions, called KkSchur functions, whose highest degree term is a kSchur function. The dual basis in Kcohomology is given by the affine stable Grothendieck polynomials, verifying a conjecture of Lam. In addition, we give a Pieri rule in Khomology. Many of our constructions have geometric interpretations using Kashiwara's thick affine flag manifold.
 Publication:

arXiv eprints
 Pub Date:
 January 2009
 arXiv:
 arXiv:0901.1506
 Bibcode:
 2009arXiv0901.1506L
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Algebraic Geometry;
 05E05;
 14N15
 EPrint:
 38 pages