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  • 1
    Electronic Resource
    Electronic Resource
    Structure of some ℤ-graded lie superalgebras of vector fields (1999)
    Springer
    Transformation groups 4 (1999), S. 219-272 
    Details
    ISSN: 1531-586X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we classifyℤ-graded transitive Lie superalgebras with prescribed nonpositive parts listed in [K2]. The classification of infinite-dimensional simple linearly compact Lie superalgebras given in [K2] is based on this result. We also study the structure of the exceptionalℤ-graded transitive Lie superalgebras and give their geometric realization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01237358
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    Paper (German National Licenses)
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  • 2
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    Irreducible characters of Kac-Moody Lie superalgebras (2014)
    Oxford University Press
    Details
    Publication Date: 2014-12-27
    Description: Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$ , we establish an equivalence between parabolic Bernstein-Gelfand-Gelfand (BGG) categories of a Kac–Moody Lie superalgebra and a Kac–Moody Lie algebra. The characters for a large family of irreducible highest weight modules over a symmetrizable Kac–Moody Lie superalgebra are then given in terms of Kazhdan–Lusztig polynomials for the first time. We formulate a notion of integrable modules over a symmetrizable Kac–Moody Lie superalgebra via super duality, and show that these integrable modules form a semisimple tensor subcategory, whose Littlewood–Richardson tensor product multiplicities coincide with those in the Kac–Moody Lie algebra setting.
    Print ISSN: 0024-6115
    Electronic ISSN: 1460-244X
    Topics: Mathematics
    Published by Oxford University Press
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