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Equivariant $K$-homology of affine Grassmannian and $K$-theoretic double $k$-Schur functions
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abstract
We study the torus equivariant K-homology ring of the affine Grassmannian $\mathrm{Gr}_G$ 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 $\mathrm{Gr}_{{SL}_n}$ as the coordinate ring of a centralizer family for $PGL_n(\mathbb{C})$.
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Cited by 1 Pith paper
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Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian
The authors explicitly realize the equivariant K-Peterson map for SL_n by a rational substitution and prove a factorization formula for K-theoretic double k-Schur functions.
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