{"paper":{"title":"Finite-dimensional representations of the elliptic modular double","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"S. E. Derkachov, V. P. Spiridonov","submitted_at":"2013-10-28T13:05:19Z","abstract_excerpt":"We investigate the kernel space of an integral operator M(g) depending on the \"spin\" g and describing an elliptic Fourier transformation. The operator M(g) is an intertwiner for the elliptic modular double formed from a pair of Sklyanin algebras with the parameters $\\eta$ and $\\tau$, Im$ \\tau>0$, Im$\\eta>0$. For two-dimensional lattices $g=n\\eta + m\\tau/2$ and $g=1/2+n\\eta + m\\tau/2$ with incommensurate $1, 2\\eta,\\tau$ and integers $n,m>0$, the operator M(g) has a finite-dimensional kernel that consists of the products of theta functions with two different modular parameters and is invariant u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7570","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":""},"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"}