{"paper":{"title":"Howe duality and dynamical Weyl group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Giovanni Felder (ETH Zurich), Rea Dalipi (University of Geneva)","submitted_at":"2022-08-27T16:55:56Z","abstract_excerpt":"We give a fermionic formula for $R$-matrices of exterior powers of the vector representations of $U_q(\\widehat{ \\mathfrak{gl}}_N)$ and relate it to the dynamical Weyl group of Tarasov--Varchenko and Etingof--Varchenko, via a Howe ($\\mathfrak{gl}_N,\\mathfrak{gl}_M)$-duality. In the limit $N\\to\\infty$ we obtain $R$-matrices for Fock spaces. As a consequence of our result we obtain a dynamical action of the Weyl group on integrable $U_q\\mathfrak{gl}_M$-modules, extending the known action on zero weight spaces. In an Appendix by Anfisa Gurenkova it is shown that the latter property also holds if w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.13055","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/2208.13055/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"}