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A bound on the complexity for $ G\sb rT$ modules

Author: Daniel K. Nakano
Journal: Proc. Amer. Math. Soc. 123 (1995), 335-341
MSC: Primary 17B55; Secondary 17B50, 20G05
MathSciNet review: 1242099
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Abstract: For group algebras the complexity of a module can be computed by looking at its restriction to elementary abelian subgroups. This statement is not true for modules over the restricted enveloping algebras of a restricted Lie algebra. Let G be a connected semisimple group scheme and $ {G_r}$ be the rth Frobenius kernel. In this paper an upper bound on the complexity is provided for $ {G_1}T$ modules. Furthermore, a bound is given for the complexity of a simple $ {G_r}$ module, $ L(\lambda )$, by the complexities of the simple $ {G_1}$ modules in the tensor product decomposition of $ L(\lambda )$.

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