Weight modules of D(2,1, α)

Crystal Hoyt

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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-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 languageEnglish
Pages (from-to)91-100
Number of pages10
JournalSpringer INdAM Series
Volume7
DOIs
StatePublished - 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, Springer International Publishing Switzerland.

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