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Complexity for modules over the classical Lie superalgebra
Published online by Cambridge University Press: 25 July 2012
Abstract
Let be a classical Lie superalgebra and let ℱ be the category of finite-dimensional -supermodules which are completely reducible over the reductive Lie algebra . In [B. D. Boe, J. R. Kujawa and D. K. Nakano, Complexity and module varieties for classical Lie superalgebras, Int. Math. Res. Not. IMRN (2011), 696–724], we demonstrated that for any module M in ℱ the rate of growth of the minimal projective resolution (i.e. the complexity of M) is bounded by the dimension of . In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra . In both cases we show that the complexity is related to the atypicality of the block containing the module.
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- Copyright © Foundation Compositio Mathematica 2012
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