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.

N1 - Funding Information:
2 Alexander von Humboldt Fellow, on leave from Physics Dept., Bo~aziqi University, Istanbul/Turkey. Work supported in part by TBTAK, the National Science and Technology Council of Turkey.
Funding Information:
We would like to thank I. Bars, F. Giirsey, S. MacDowell, W. Schmid, G. Seligman and G. Zuckerman for useful discussions, Our special thanks are due to R. Langlands for several enlightening discussions and for pointing out the importance of 3 dimensional graded structure for the holomorphic discrete series representations. One of us (M.G.) would like to thank Yale University for its hospitality 'where part of this work was done and the Deutsche For-schungsgemeinschaft for a travel grant. C.S. gratefully acknowledges an Alexander von Humboldt Stiftung fellowship and the partial support by TBTAK, and thanks the Bonn Physics Department for its hospitality.

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

SN - 0370-2693

VL - 108

SP - 180

EP - 186

JO - Physics Letters B

JF - Physics Letters B

IS - 3

ER -