{"paper":{"title":"The $[n_1,n_2,\\ldots,n_s]$--th reduced KP hierarchy and $W_{1+\\infty}$ constraints","license":"","headline":"","cross_cats":["math.QA","q-alg"],"primary_cat":"hep-th","authors_text":"Johan van de Leur","submitted_at":"1994-11-10T09:56:55Z","abstract_excerpt":"To every partition $n=n_1+n_2+\\cdots+n_s$ one can associate a vertex operator realization of the Lie algebras $a_{\\infty}$ and $\\hat{gl}_n$. Using this construction we obtain reductions of the $s$--component KP hierarchy, reductions which are related to these partitions. In this way we obtain matrix KdV type equations. We show that the following two constraints on a KP $\\tau$--function are equivalent (1) $\\tau$ is a $\\tau$--function of the $[n_1,n_2,\\ldots,n_s]$--th reduced KP hierarchy which satisfies string equation, $L_{-1}\\tau=0$, (2) $\\tau$ satisfies the vacuum constraints of the $W_{1+\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9411071","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"}