Equivariant oriented homology of the affine Grassmannian

2023/01/30 by Changlong Zhong, Zhong, Changlong
Mathematics · #14F43 #14M15 #14N15 #19L41 #55N22 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2301.13056

openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the property of small-torus equivariant K-homology of the affine Grassmannian to general oriented (co)homology theory in the sense of Levine and Morel. The main tool we use is the formal affine Demazure algebra associated to the affine root system. More precisely, we prove that the small-torus equivariant oriented cohomology of the affine Grassmannian satisfies the GKM condition. We also show that its dual, the small-torus equivariant homology, is isomorphic to the centralizer of the equivariant oriented cohomology of a point in the the formal affine Demazure algebra.

Related

• Equivariant K-homology of affine Grassmannian and K-theoretic double k-Schur functions
• Introduction to Equivariant Cohomology in Algebraic Geometry (IMPANGA 2010)
• Localization of equivariant cohomology rings of real Grassmannians
• Equivariant K-theory, affine Grassmannian and perfection
• The Leray-Hirsch Theorem for equivariant oriented cohomology of flag varieties