Abstract
Let g be a basic Lie superalgebra. A weight module M over g is called finite if all of its weight spaces are finite dimensional, and it is called bounded if there is a uniform bound on the dimension of a weight space. The minimum bound is called the degree of M. For g = D(2,1, α), we prove that every simple weight module M is bounded and has degree less than or equal to 8. This bound is attained by a cuspidal module M if and only if M belongs to a \((g,{g_{\bar 0}})\)-coherent family \(L(\lambda )_\Gamma ^\mu \) for some typical module L (λ). Cuspidal modules which correspond to atypical modules have degree less than or equal to 6 and greater than or equal to 2.
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Hoyt, C. (2014). Weight modules of D(2,1, α). In: Gorelik, M., Papi, P. (eds) Advances in Lie Superalgebras. Springer INdAM Series, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02952-8_6
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DOI: https://doi.org/10.1007/978-3-319-02952-8_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02951-1
Online ISBN: 978-3-319-02952-8
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