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Irreducibility of the ladder representations of \(U(2,2)\) when restricted to the Poincaré subgroup. (English) Zbl 0183.29003

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.

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations
22E70 Applications of Lie groups to the sciences; explicit representations
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