{"paper":{"title":"Regular Conjugacy Classes in the Weyl Group and Integrable Hierarchies","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"F. Delduc, L. Feher","submitted_at":"1994-10-27T13:02:58Z","abstract_excerpt":"Generalized KdV hierarchies associated by Drinfeld-Sokolov reduction to grade one regular semisimple elements from non-equivalent Heisenberg subalgebras of a loop algebra $\\G\\otimes{\\bf C}[\\lambda,\\lambda^{-1}]$ are studied. The graded Heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the Weyl group ${\\bf W}(\\G)$ of the simple Lie algebra $\\G$. A representative $w\\in {\\bf W}(\\G)$ of a regular conjugacy class can be lifted to an inner automorphism of $\\G$ given by $\\hat w=\\exp\\left(2i\\pi {\\rm ad I_0}/m\\right)$, where $I_0$ is the defining vector of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9410203","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"}