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  • 1
    Electronic Resource
    Electronic Resource
    Transformations of some induced osp(3/2) modules in an so(3)⊕sp(2) basis (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1841-1863 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The modules of the orthosymplectic Lie superalgebra osp(3/2), induced from finite-dimensional irreducible submodules of the stability subalgebra so(3)⊕gl(1) are investigated. The corresponding infinite-dimensional irreducible or indecomposable modules, the Kac modules, and the related typical and atypical modules are studied in detail. Every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so(3)⊕sp(2). For each of these (infinite-dimensional or finite-dimensional, irreducible or indecomposable) modules relations are written down, giving the transformations of the basis under the action of the algebra generators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529662
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  • 2
    Electronic Resource
    Electronic Resource
    Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. I. Typical representations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 553-570 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: 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)&supuline;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 Vi, 1≤i≤16. The basis Γ in W is chosen to consist of the union of all Γi, where Γi is an appropriate basis in each Vi. 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528421
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  • 3
    Electronic Resource
    Electronic Resource
    Induced representations of the two parametric quantum deformation Upq[gl(2/2)] (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 6487-6508 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The two-parametric quantum superalgebra Up,q[gl(2/2)] and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in detail. It turns out that finite-dimensional representations of the two-parametric Up,q[gl(2/2)], even at generic deformation parameters, are not simply trivial deformations from those of the classical superalgebra gl(2/2), unlike the one-parametric cases. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1286510
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  • 4
    Electronic Resource
    Electronic Resource
    Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]. I. Typical representations at generic q (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2583-2606 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the present paper all typical finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)] are constructed at generic deformation parameter q. As in the nondeformed case, the finite-dimensional Uq[gl(2/2)]-module Wq obtained is irreducible and can be decomposed into finite-dimensional irreducible Uq[gl(2)⊕gl(2)]-submodules Vqk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530525
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  • 5
    Electronic Resource
    Electronic Resource
    Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]. II. Nontypical representations at generic q (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 5979-6003 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The construction approach proposed in the previous paper [N. A. Ky, J. Math. Phys. 35, 2583 (1994)] allows us there and in the present paper to construct at generic deformation parameter q all finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)]. The finite-dimensional Uq[gl(2/2)]-modules Wq constructed in the previous paper are either irreducible or indecomposable. If a module Wq is indecomposable, i.e., when the condition (4.41) in the previous paper does not hold, there exists an invariant maximal submodule of Wq, say, Iqk, such that the factor representation in the factor module Wq/Iqk is irreducible and called nontypical. Here, in this paper, indecomposable representations and nontypical finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)] are considered and classified as their module structures are analyzed and the matrix elements of all nontypical representations are written down explicitly. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531231
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