{"paper":{"title":"D-functions and immanants of unitary matrices and submatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Dylan Spivak, Hubert de Guise, Ish Dhand, Justin Kulp","submitted_at":"2015-11-05T18:47:31Z","abstract_excerpt":"Motivated by recent results in multiphoton interferometry, we expand a result of Kostant on immanants of an arbitrary $m\\times m$ unitary matrix $T\\in$ su$(m)$ to the submatrices of $T$. Specifically, we show that immanants of principal submatrices of a unitary matrix $T$ are a sum $\\sum_{t} D^{(\\lambda)}_{tt}(\\Omega)$ of the diagonal $D$-functions of group element $\\Omega$, with $t$ determined {by} the choice of submatrix, and the irrep $(\\lambda)$ determined by the immanant under consideration. We also provide evidence that this result extends to some submatrices that are not principal diago"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01851","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"}