{"paper":{"title":"QES systems, invariant spaces and polynomials recursions","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"B. Prasad Mandal, J. Ndimubandi, Y. Brihaye","submitted_at":"2006-01-02T13:03:08Z","abstract_excerpt":"Let us denote ${\\cal V}$, the finite dimensional vector spaces of functions of the form $\\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$ represents a fixed function of $x$.\n  Conditions on $m,n$ and $f(x)$ are found such that families of linear differential operators exist which preserve ${\\cal V}$. A special emphasis is accorded to the cases where the set of differential operators represents the envelopping algebra of some abstract algebra. These operators can be transformed into linear matrix"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0601004","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"}