A bound on the complexity for 𝐺ᵣ𝑇 modules

Nakano, Daniel K.

doi:10.1090/S0002-9939-1995-1242099-7

A bound on the complexity for $G_ rT$ modules
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by Daniel K. Nakano PDF

Proc. Amer. Math. Soc. 123 (1995), 335-341 Request permission

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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