{"paper":{"title":"Dynamical elliptic Bethe algebra, KZB eigenfunctions, and theta-polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.MP","math.QA"],"primary_cat":"math-ph","authors_text":"Alexander Varchenko, Daniel Thompson","submitted_at":"2018-10-21T18:22:07Z","abstract_excerpt":"Let $(\\otimes_{j=1}^nV_j)[0]$ be the zero weight subspace of a tensor product of finite-dimensional irreducible $\\frak{sl}_2$-modules. The dynamical elliptic Bethe algebra is a commutative algebra of differential operators acting on $(\\otimes_{j=1}^nV_j)[0]$-valued functions on the Cartan subalgebra of $\\frak{sl}_2$. The algebra is generated by values of the coefficient $S_2(x)$ of a certain differential operator $D=(d/dx)^2+S_2(x)$, defined to V. Rubtsov, A. Silantyev, D. Talalaev in 2009. We express $S_2(x)$ in terms of the KZB operators introduced by G. Felder and C. Wieszerkowski in 1994. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09001","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":""},"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"}