k-Double Schur functions and equivariant (co)homology of the affine Grassmannian

Abstract

The Schubert bases of the torus-equivariant homology and cohomology rings of the affine Grassmannian of the special linear group are realized by new families of symmetric functions called k-double Schur functions and affine double Schur functions.

arXiv comment24 pages

References in corpus (2)

• Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras
• k-shape poset and branching of k-Schur functions

Cited by in corpus (4)

• From double quantum Schubert polynomials to k-double Schur functions via the Toda lattice
• Universal factorial Schur $P,Q$-functions and their duals
• Generalized (co)homology of the loop spaces of classical groups and the universal factorial Schur $P$- and $Q$-functions
• Equivariant Pieri Rule for the homology of the affine Grassmannian