Equivariant K-homology of affine Grassmannian and K-theoretic double k-Schur functions

2024/08/20 by Takeshi Ikeda, Mark Shimozono, Ikeda, Takeshi +3 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.10956

openalex publication_date 2024/08/20 · openalex created_date 2024/10/01 · openalex updated_date 2026/07/28

Abstract

We study the torus equivariant K-homology ring of the affine Grassmannian Gr_G where G is a connected reductive linear algebraic group. In type A, we introduce equivariantly deformed symmetric functions called the K-theoretic double k-Schur functions as the Schubert bases. The functions are constructed by Demazure operators acting on equivariant parameters. As an application, we provide a Ginzburg-Peterson type realization of the torus-equivariant K-homology ring of Gr_SL_n as the coordinate ring of a centralizer family for PGL_n(ℂ).

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