{"paper":{"title":"Quantum $K$-theory of Lagrangian Grassmannian via parabolic Peterson isomorphism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.KT","math.RT"],"primary_cat":"math.AG","authors_text":"Kohei Yamaguchi, Takafumi Kouno, Takeshi Ikeda, Yusuke Nakayama","submitted_at":"2024-05-28T06:13:32Z","abstract_excerpt":"We study Schubert calculus in the torus-equivariant quantum $K$-ring of the Lagrangian Grassmannian $\\mathrm{LG}(n)$. Our main tool is the $K$-theoretic Peterson map due to Kato. The map is from the (localized) equivariant $K$-homology ring $K_{*}^{T}(\\mathrm{Gr}_{G})$ of the affine Grassmannian $\\mathrm{Gr}_{G}$ of the symplectic group $G=\\mathrm{Sp}_{2n}(\\mathbb{C})$ to the (localized) torus-equivariant quantum $K$-ring $QK_{T}(\\mathrm{LG}(n))$. We determine explicitly the kernel of this map."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.17854","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/2405.17854/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"}