TY - JOUR

T1 - Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

AU - Günaydin, M.

AU - Saçlioǧlu, C.

PY - 1982/1/21

Y1 - 1982/1/21

N2 - We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups SP(2n, R and SO(2n)* from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n≥4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)* and E7(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E7(7) and SO(12)* obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)*.

AB - We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups SP(2n, R and SO(2n)* from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n≥4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)* and E7(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E7(7) and SO(12)* obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)*.

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U2 - 10.1016/0370-2693(82)91170-4

DO - 10.1016/0370-2693(82)91170-4

M3 - Article

AN - SCOPUS:4244040064

VL - 108

SP - 180

EP - 186

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 3

ER -