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  • 1
    Electronic Resource
    Electronic Resource
    The quantum super-Yangian and Casimir operators of Uq(gl(M |N)) (1995)
    Springer
    Letters in mathematical physics 33 (1995), S. 263-272 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 17A70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract TheZ 2 graded Yangian Yq(gl(M |N)) associated with the Perk-SchultzR matrix is introduced. Its structural properties, the central algebra in particular, are studied. AZ 2-graded associative algebra epimorphism Yq(gl(M |N)) → Uq (gl(M |N)) is obtained in explicit form. Images of central elements of the quantum super-Yangian under this epimorphism yield the Casimir operators of the quantum supergroup Uq(gl(M |N)) constructed in an earlier publication.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00749628
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  • 2
    Electronic Resource
    Electronic Resource
    Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1) (1992)
    Springer
    Letters in mathematical physics 25 (1992), S. 317-325 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 17A70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the quantum supergroup U q (osp(1/2n)) is essentially isomorphic to the quantum group U -q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398404
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  • 3
    Electronic Resource
    Electronic Resource
    The gl (M|N) super Yangian and its finite-dimensional representations (1996)
    Springer
    Letters in mathematical physics 37 (1996), S. 419-434 
    Details
    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 17A70 ; super Yangian ; irreducible highest weight representations ; Lie superalgebra ; Hopf algebra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Methods are developed for systematically constructing the finite-dimensional irreducible representations of the super Yangian Y (gl(M|N)) associated with the Lie superalgebra gl(M|N). It is also shown that every finite-dimensional irreducible representation of Y (gl(M|N)) is of highest weight type, and is uniquely characterized by a highest weight. The necessary and sufficient conditions for an irrep to be finite-dimensional are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00312673
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