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

Van der Jeugt, J.

doi:10.1063/1.526061

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

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

Nov, 1984

15 pages

Published in:

J.Math.Phys. 25 (1984) 3334-3349

DOI:

10.1063/1.526061

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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 orthosymplectic superalgebra osp(3,2). For all cases, the star or grade star conditions for the algebra are investigated. Only two finite‐dimensional representations are grade star representations, if the representation space is required to be a graded Hilbert space. When the even part is so(3)⊕sp(2,R)≊su(2)⊕su(1,1), an infinite class of infinite‐dimensional star representations is found. One of them can be realized in terms of two‐valued functions of a complex variable. This representation reduces to the sum of two metaplectic representations of sp(2). We show that it is precisely this ‘‘metaplectic representation for osp(3,2)’’ which gives the spin‐energy eigenstates for the one‐dimensional harmonic oscillator with spin 1/2 states.

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