@article{gomez-ullateQuasiexactSolvabilityGeneral2007,
 abstract = {Our goal in this paper is to extend the theory of quasi-exactly solvable Schrödinger operators beyond the Lie-algebraic class. Let  be the space of nth degree polynomials in one variable. We first analyze exceptional polynomial subspaces , which are those proper subspaces of  invariant under second-order differential operators which do not preserve . We characterize the only possible exceptional subspaces of codimension one and we describe the space of second-order differential operators that leave these subspaces invariant. We then use equivalence under changes of variable and gauge transformations to achieve a complete classification of these new, non-Lie algebraic Schrödinger operators. As an example, we discuss a finite gap elliptic potential which does not belong to the Treibich--Verdier class.},
 author = {Gómez-Ullate, D and Kamran, N and Milson, R},
 doi = {10.1088/0266-5611/23/5/008},
 file = {/Users/david/Zotero/storage/8MSVPCUF/Gómez-Ullate et al. - 2007 - Quasi-exact solvability in a general polynomial setting.pdf},
 issn = {0266-5611, 1361-6420},
 journal = {Inverse Problems},
 month = {October},
 number = {5},
 pages = {1915--1942},
 title = {Quasi-Exact Solvability in a General Polynomial Setting},
 urldate = {2025-10-19},
 volume = {23},
 year = {2007}
}