{"paper":{"title":"On the Existence of Generalized Parking Spaces for Complex Reflection Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Soichi Okada, Yosuke Ito","submitted_at":"2015-08-27T13:14:06Z","abstract_excerpt":"Let $W$ be an irreducible finite complex reflection group acting on a complex vector space $V$. For a positive integer $k$, we consider a class function $\\varphi_k$ given by $\\varphi_k(w) = k^{\\dim V^w}$ for $w \\in W$, where $V^w$ is the fixed-point subspace of $w$. If $W$ is the symmetric group of $n$ letters and $k=n+1$, then $\\varphi_{n+1}$ is the permutation character on (classical) parking functions. In this paper, we give a complete answer to the question when $\\varphi_k$ (resp. its $q$-analogue) is the character of a representation (resp. the graded character of a graded representation)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06846","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"}