Quasi-Exactly-Solvable Differential Equations
| dc.creator | Turbiner, Alexander | |
| dc.date | 1994-09-12 | |
| dc.date | 1994-10-12 | |
| dc.date.accessioned | 2026-07-07T09:03:45Z | |
| dc.date.available | 2026-07-07T09:03:45Z | |
| dc.description | A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a representation as a polynomial element of the universal enveloping algebra of the algebra of differential (difference) operators in finite-dimensional representation. In one-dimensional case a classification is given by algebras $sl_2({\bold R})$ (for differential operators in ${\bold R}$) and $sl_2({\bold R})_q$ (for finite-difference operators in ${\bold R}$), $osp(2,2)$ (operators in one real and one Grassmann variable, or equivalently, $2 \times 2$ matrix operators in ${\bold R}$) and $gl_2 ({\bold R})_K$ ( for the operators containing the differential operators and the parity operator). A classification of linear operators possessing infinitely many finite-dimensional invariant subspaces with a basis in polynomials is presented. | |
| dc.description | 33 pages, to appear as Chapter 12 in CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3 : New Trends in Theoretical Developments and Computational Methods, ed. N. H. Ibragimov, CRC Press, 1995 | |
| dc.identifier | https://arxiv.org/abs/hep-th/9409068 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9409068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149130 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Functional Analysis | |
| dc.title | Quasi-Exactly-Solvable Differential Equations | |
| dc.type | text |