{"paper":{"title":"Equivariant $K$-homology of affine Grassmannian and $K$-theoretic double $k$-Schur functions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG","math.CO","math.KT"],"primary_cat":"math.RT","authors_text":"Kohei Yamaguchi, Mark Shimozono, Takeshi Ikeda","submitted_at":"2024-08-20T15:51:13Z","abstract_excerpt":"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 $PGL_n(\\mathbb{C})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10956","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.10956/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}