IRREDUCIBLE REPRESENTATIONS OF THE EXCEPTIONAL LIE SUPERALGEBRAS D(2,1 :ALPHA) - INSPIRE

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IRREDUCIBLE REPRESENTATIONS OF THE EXCEPTIONAL LIE SUPERALGEBRAS D(2,1 :ALPHA)

J. Van Der Jeugt
(
- Queen Mary, U. of London
)

1985

12 pages

Published in:

J.Math.Phys. 26 (1985) 913-924

DOI:

10.1063/1.526547

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Abstract: (AIP)

The shift operator technique is used to give a complete analysis of all finite‐ and infinite‐dimensional irreducible representations of the exceptional Lie superalgebrasD(2,1;α). For all cases, the star or grade star conditions for the algebra are investigated. Among the finite‐dimensional representations there are no star and only a few grade star representations, but an infinite class of infinite‐dimensional star representations is found. Explicit expressions are given for the ‘‘doublet’’ representation of D(2,1;α). The one missing label problem D(2,1;α)→su(2)+su(2)+su(2) is discussed in detail and solved explicitly.

ALGEBRA: LIE
ALGEBRA: REPRESENTATION
ALGEBRA: D(2,1:ALPHA)
SUPERSYMMETRY

References(16)

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Representations of Supergroups

A. Baha Balantekin
(
- Yale U.
)
,
Itzhak Bars
(
- Yale U.
)

- J.Math.Phys. 22 (1981) 1810,
- J. Math. Phys. 22 ( 1981) 1810-1818 and Yale Univ. New Haven - YTP-80-36 (80,REC.MAR. 81) 38p
•
DOI:
- 10.1063/1.525127

Graded Lie Algebras in Mathematics and Physics (Bose-Fermi Symmetry)

- Rev.Mod.Phys. 47 (1975) 573,
•
DOI:
- 10.1103/RevModPhys.47.573

Explicit Construction of the Exceptional Superalgebras F(4) and $G$ (3)

Bryce S. DeWitt
(
- Texas U. and
- Santa Barbara, KITP
)
,
Peter van Nieuwenhuizen
(
- SUNY, Stony Brook
)

- J.Math.Phys. 23 (1982) 1953
•
DOI:
- 10.1063/1.525246

Representations of Low Rank Orthosymplectic Superalgebras by Superfield Techniques

R.J. Farmer
(
- Tasmania U.
)
,
Peter D. Jarvis
(
- Tasmania U.
)

- J.Phys.A 16 (1983) 473
•
DOI:
- 10.1088/0305-4470/16/3/008

IRREDUCIBLE REPRESENTATIONS OF SUPERALGEBRAS B(1,1) AND B(0,2)

Qi-Zhi Han
(
- Peking U.
)
,
Hong-Zhou Sun
(
- Peking U.
)

- Commun.Theor.Phys. 2 (1983) 1137-1144,
- Commun. Theor. Phys. 2 ( 1983) 1137-1144

O(3) Shift Operators. 1. The General Analysis

J.W.B. Hughes
(
- Queen Mary, U. of London
)
,
J. Yadegar
(
- Cambridge U.
)

- J.Math.Phys. 19 (1978) 2068
•
DOI:
- 10.1063/1.523587

Representations of Osp(2,1) and the Metaplectic Representation

J.W.B. Hughes
(
- Queen Mary, U. of London
)

- J.Math.Phys. 22 (1981) 245-250,
- J. Math. Phys. 22 ( 1981) 245-250
•
DOI:
- 10.1063/1.524895

Irreducible Representations of SU( $M/N$ )

J.P. Hurni
(
- Geneva U.
)
,
B. Morel
(
- Geneva U.
)

- J.Math.Phys. 24 (1983) 157,
- J.Math.Phys. 24 (1983) 2250 (erratum)
•
DOI:
- 10.1063/1.525573

Lie Superalgebras

V.G. Kac
(
- MIT, LNS
)

- Adv.Math. 26 (1977) 8-96
•
DOI:
- 10.1016/0001-8708(77)90017-2

A Sketch of Lie Superalgebra Theory

V.G. Kac
(
- Moscow Electronic Machinery Inst.
)

- Commun.Math.Phys. 53 (1977) 31-64
•
DOI:
- 10.1007/BF01609166

- Lect.Notes Math. 676 597

Classification of All Simple Graded Lie Algebras Whose Lie Algebra Is Reductive. 1.

- J.Math.Phys. 17 (1976) 1626
•
DOI:
- 10.1063/1.523108

Graded Lie Algebras: Generalization of Hermitian Representations

- J.Math.Phys. 18 (1977) 146
•
DOI:
- 10.1063/1.523148

- Lett.Nuovo Cim. 33 120

SHIFT OPERATOR APPROACH OF THE SPIN - ISOSPIN SUPERMULTIPLET STATE LABELING PROBLEM: EIGENVALUE DETERMINATION OF THE OMEGA AND PHI LABELING OPERATORS

- Annals Phys. 147 (1983) 85-139,
- Ann. Phys. ( N.y.) 147 ( 1983) 85-139
•
DOI:
- 10.1016/0003-4916(83)90068-4

Finite and infinite-dimensional representations of the orthosymplectic superalgebra OSP(3,2)

J. Van der Jeugt
(
- Queen Mary, U. of London
)

- J.Math.Phys. 25 (1984) 3334-3349
•
DOI:
- 10.1063/1.526061