Equivariant $K$-homology of affine Grassmannian and $K$-theoretic double $k$-Schur functions
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 $PGL_n(\mathbb{C})$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.10956
- arXiv:
- arXiv:2408.10956
- Bibcode:
- 2024arXiv240810956I
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Algebraic Geometry;
- Mathematics - Combinatorics;
- Mathematics - K-Theory and Homology
- E-Print:
- 47 pages