{"paper":{"title":"On the Quantum K-theory of Quiver Varieties at Roots of Unity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP","math.NT","math.RT"],"primary_cat":"math.AG","authors_text":"Andrey Smirnov, Peter Koroteev","submitted_at":"2024-12-26T23:52:58Z","abstract_excerpt":"Let $\\Psi(\\textbf{z},\\textbf{a},q)$ a the fundamental solution matrix of the quantum difference equation of a Nakajima variety $X$. In this work, we prove that the operator $$ \\Psi(\\textbf{z},\\textbf{a},q) \\Psi\\left(\\textbf{z}^p,\\textbf{a}^p,q^{p^2}\\right)^{-1} $$ has no poles at the primitive complex $p$-th roots of unity $q=\\zeta_p$. As a byproduct, we show that the iterated product of the operators ${\\bf M}_{\\mathcal{L}}(\\textbf{z},\\textbf{a},q )$ from the $q$-difference equation on $X$: $$ {\\bf M}_{\\mathcal{L}} (\\textbf{z} q^{(p-1)\\mathcal{L}},\\textbf{a},q) \\cdots {\\bf M}_{\\mathcal{L}} (\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19383","kind":"arxiv","version":4},"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/2412.19383/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"}