Finite dimensional representations of the Lie superalgebra gl(2/2) in a gl(2) x gl(2) basis. 1. Typical representations - INSPIRE

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Finite dimensional representations of the Lie superalgebra gl(2/2) in a gl(2) x gl(2) basis. 1. Typical representations

A.H. Kamupingene
(
- Sofiya U.
)
,
Nguyen Anh Ky
(
- Sofiya U.
)
,
T.D. Palev
(
- Sofiya, Inst. Nucl. Res.
)

1989

18 pages

Published in:

J.Math.Phys. 30 (1989) 553-570

DOI:

10.1063/1.528421

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Abstract: (AIP)

In a series of two papers all finite‐dimensional irreducible representations and some indecomposible representations of the general linear Lie superalgebra gl(2/2) are constructed in a basis suitable for the decomposition gl(2/2)⊇gl(2)⊕gl(2). In this paper each induced gl(2/2) module W is represented as a direct sum of its irreducible gl(2)⊕gl(2) submodules V i , 1≤i≤16. The basis Γ in W is chosen to consist of the union of all Γ i , where Γ i is an appropriate basis in each V i . Expressions for the transformation of Γ under the action of the generators are written down for all induced and hence, also, for all typical gl(2/2) modules.

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