{"paper":{"title":"Infinitely many commuting operators for the elliptic quantum group $U_{q,p}(\\hat{sl_N})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Takeo Kojima","submitted_at":"2011-01-21T08:15:53Z","abstract_excerpt":"We construct two classes of infinitely many commuting operators associated with the elliptic quantum group $U_{q,p}(\\hat{sl_N})$. We call one of them the integral of motion ${\\cal G}_m$, $(m \\in {\\mathbb N})$ and the other the boundary transfer matrix $T_B(z)$, $(z \\in {\\mathbb C})$. The integral of motion ${\\cal G}_m$ is related to elliptic deformation of the $N$-th KdV theory. The boundary transfer matrix $T_B(z)$ is related to the boundary $U_{q,p}(\\hat{sl_N})$ face model. We diagonalize the boundary transfer matrix $T_B(z)$ by using the free field realization of the elliptic quantum group,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4084","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"}