{"paper":{"title":"Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.CO","math.KT"],"primary_cat":"math.RT","authors_text":"Kohei Yamaguchi, Satoshi Naito, Shinsuke Iwao, Takeshi Ikeda","submitted_at":"2025-05-05T18:18:34Z","abstract_excerpt":"We investigate the phenomenon known as ''quantum equals affine'' in the setting of $T$-equivariant quantum $K$-theory of the flag variety $G/B$, as established by Kato for any semisimple algebraic group $G$. In particular, we focus on the $K$-Peterson isomorphism between the $T$-equivariant quantum $K$-ring $QK_T(\\mathrm{SL}_n(\\mathbb{C})/B)$ and the $T$-equivariant $K$-homology ring $K_*^T(\\mathrm{Gr}_{\\mathrm{SL}_n})$ of the affine Grassmannian, after suitable localizations on both sides. Building on an earlier work by Ikeda, Iwao, and Maeno, we present an explicit algebraic realization of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02941","kind":"arxiv","version":3},"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/2505.02941/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"}