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,g0¯-coherent family LλΓμ 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.
Original language | English |
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Pages (from-to) | 91-100 |
Number of pages | 10 |
Journal | Springer INdAM Series |
Volume | 7 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2014, Springer International Publishing Switzerland.