{"paper":{"title":"Coherent states on the Grassmannian $U(4)/U(2)^2$: Oscillator realization and bilayer fractional quantum Hall systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"E. Perez-Romero, M. Calixto","submitted_at":"2013-12-11T12:59:36Z","abstract_excerpt":"Bilayer quantum Hall (BLQH) systems, which underlie a $U(4)$ symmetry, display unique quantum coherence effects. We study coherent states (CS) on the complex Grassmannian $\\mathbb G_2^4=U(4)/U(2)^2$, orthonormal basis, $U(4)$ generators and their matrix elements in the reproducing kernel Hilbert space $\\mathcal H_\\lambda(\\mathbb G_2^4)$ of analytic square-integrable holomorphic functions on $\\mathbb G_2^4$, which carries a unitary irreducible representation of $U(4)$ with index $\\lambda\\in\\mathbb N$. A many-body representation of the previous construction is introduced through an oscillator re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3148","kind":"arxiv","version":2},"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"}