Mack, G.; Todorov, I. Irreducibility of the ladder representations of \(U(2,2)\) when restricted to the Poincaré subgroup. (English) Zbl 0183.29003 J. Math. Phys. 10, 2078-2085 (1969). Summary: It is shown that the most degenerate discrete series of unitary irreducible representations of \(U(2,2)\), the so-called ladder representations, remain irreducible when restricted to representations of the Poincaré subgroup \(\mathrm{ISL}(2,\mathbb C)\). They correspond to representations of this subgroup with mass zero and arbitrary integer or half-integer helicity \(\lambda\). The basis vectors of the canonical basis are calculated as functions of a lightlike 4-vector, which is formed by the simultaneous eigenvalues of the generators of the subgroup of translations. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 42 Documents MSC: 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 22E70 Applications of Lie groups to the sciences; explicit representations PDF BibTeX XML Cite \textit{G. Mack} and \textit{I. Todorov}, J. Math. Phys. 10, 2078--2085 (1969; Zbl 0183.29003) Full Text: DOI OpenURL References: [1] DOI: 10.2307/1968455 · Zbl 0014.08004 [2] DOI: 10.1103/PhysRev.150.1183 [3] DOI: 10.1103/PhysRev.150.1183 [4] DOI: 10.1103/PhysRev.150.1183 [5] DOI: 10.1103/PhysRev.150.1183 [6] DOI: 10.1016/0550-3213(68)90232-0 [7] Flato M., Compt. Rend. 263 pp 935– (1966) [8] DOI: 10.1063/1.1705108 · Zbl 0171.23902 [9] DOI: 10.1143/PTPS.37.368 [10] DOI: 10.1143/PTPS.37.368 [11] DOI: 10.1143/PTPS.37.368 [12] DOI: 10.1143/PTPS.37.368 [13] DOI: 10.1143/PTPS.37.368 [14] DOI: 10.1103/PhysRev.161.1464 [15] DOI: 10.1063/1.1664491 · Zbl 0164.56703 [16] DOI: 10.1063/1.1664491 · Zbl 0164.56703 [17] DOI: 10.1063/1.1664491 · Zbl 0164.56703 [18] Sternheimer D., J. Math. Pure Appl. 47 pp 289– (1968) [19] DOI: 10.1007/BF01645755 · Zbl 0152.23204 [20] DOI: 10.1007/BF01645755 · Zbl 0152.23204 [21] DOI: 10.1063/1.1705410 [22] DOI: 10.1063/1.1664556 · Zbl 0169.57203 [23] Shirokov Iu. M., Zh. Eksp. Teor. Fiz. 33 pp 1208– (1957) [24] Shirokov Iu. M., Sov. Phys.–JETP 6 pp 929– (1958) [25] DOI: 10.1103/PhysRev.134.B882 [26] DOI: 10.1103/PhysRev.138.B988 [27] Castell L., Nucl. Phys. 4 pp 343– (1967) · Zbl 0162.58604 [28] Ottoson U., Arkiv Fysik 33 pp 523– (1967) · Zbl 0162.58604 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.