{"paper":{"title":"Trigonometric weight functions as K-theoretic stable envelope maps for the cotangent bundle of a flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"A. Varchenko, R. Rimanyi, V. Tarasov","submitted_at":"2014-11-03T13:18:45Z","abstract_excerpt":"We consider the cotangent bundle $T^*F_\\lambda$ of a $GL_n$ partial flag variety, $\\lambda=(\\lambda_1,...,\\lambda_N)$, $|\\lambda|=\\sum_i\\lambda_i=n$, and the torus $T=(\\C^\\times)^{n+1}$ equivariant K-theory algebra $K_T(T^*F_\\lambda)$. We introduce K-theoretic stable envelope maps $\\Stab_{\\sigma}: \\oplus_{|\\lambda|=n} K_T((T^*F_\\lambda)^T)\\to\\oplus_{|\\lambda|=n}K_T(T^*F_\\lambda)$, where $\\sigma\\in S_n$. Using these maps we define a quantum loop algebra action on $\\oplus_{|\\lambda|=n}K_T(T^*F_\\lambda)$. We describe the associated Bethe algebra $B^q(K_T(T^*F_\\lambda))$ by generators and relation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0478","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}