Unitary Irreducible Representations of SL (3, R)
- 1 July 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (7) , 1284-1294
- https://doi.org/10.1063/1.1705031
Abstract
It is shown that to each finite‐dimensional single‐valued irreducible representation of SL(3, R) there corresponds an infinite‐dimensional representation which is unitary on any member of a certain one‐parameter family of Hilbert spaces. We set up an eigenfunction problem for the members of a three‐parameter family of Hilbert subspaces on which such a unitary representation is irreducible. The relatively simple but especially important three‐dimensional case is worked out completely. Unitary irreducible representations for the unimodular real linear groups SL(N, R) with N > 3 and their subgroups can be obtained by generalizing the formalism described here.Keywords
This publication has 8 references indexed in Scilit:
- SL 3,R symmetry in the quantum theory of general relativityIl Nuovo Cimento A (1971-1996), 1966
- On non-compact groups. II. Representations of the 2+1 Lorentz groupProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1965
- Series of hadron energy levels as representations of non-compact groupsPhysics Letters, 1965
- Derivation of the Gell-Mann-Okubo Mass FormulaJournal of Mathematical Physics, 1963
- On the Representations of the Semisimple Lie Groups. I. The Explicit Construction of Invariants for the Unimodular Unitary Group in N DimensionsJournal of Mathematical Physics, 1963
- Note on Unitary Symmetry in Strong InteractionsProgress of Theoretical Physics, 1962
- Irreducible Unitary Representations of the Lorentz GroupAnnals of Mathematics, 1947
- Relativistic wave equationsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1936