On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications
| dc.creator | Lievens, S. | |
| dc.creator | Stoilova, N. I. | |
| dc.creator | Van der Jeugt, J. | |
| dc.date | 2007-01-05 | |
| dc.date.accessioned | 2026-07-07T07:52:49Z | |
| dc.date.available | 2026-07-07T07:52:49Z | |
| dc.description | In a Wigner quantum mechanical model, with a solution in terms of the Lie superalgebra gl(1|n), one is faced with determining the eigenvalues and eigenvectors for an arbitrary self-adjoint odd element of gl(1|n) in any unitary irreducible representation W. We show that the eigenvalue problem can be solved by the decomposition of W with respect to the branching gl(1|n) --> gl(1|1) + gl(n-1). The eigenvector problem is much harder, since the Gel'fand-Zetlin basis of W is involved, and the explicit actions of gl(1|n) generators on this basis are fairly complicated. Using properties of the Gel'fand-Zetlin basis, we manage to present a solution for this problem as well. Our solution is illustrated for two special classes of unitary gl(1|n) representations: the so-called Fock representations and the ladder representations. | |
| dc.identifier | https://arxiv.org/abs/math-ph/0701013 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0701013 | |
| dc.identifier | J. Phys. A: Math. Theor. 40 (2007) 3869-3888 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126017 | |
| dc.subject | Mathematical Physics | |
| dc.title | On the eigenvalue problem for arbitrary odd elements of the Lie superalgebra gl(1|n) and applications | |
| dc.type | text |