We study the local reducibility at p of the p-adic Galois representation attached to a cuspidal automorphic representation of GLn(AQ). In the case that the underlying Weil-Deligne representation is Frobenius semisimple and indecomposable, we analyze the reducibility completely. We use methods from p-adic Hodge theory, and work under a transversality assumption on the Hodge and Newton filtrations in the corresponding filtered module. © 2011 by Pacific Journal of Mathematics.

VG Narasimha Kumar Cheraku

Department of Mathematics

E. Ghate

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