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Register a new userPersitence of non degeneracy: a local analog of Iharas lemma
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Authors
Pascal Boyer
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Persitence of non degeneracy is a phenomenon which appears in the theory of $overline{mathbb Q}_l$-representations of the linear group: every irreducible submodule of the restriction to the mirabolic subgroup of an non degenerate irreducible representation is non degenerate. This is no more true in general, if we look at the modulo $l$ reduction of some stable lattice. As in the Clozel-Harris-Taylor generalization of global Iharas lemma, we show that this property, called non degeneracy persitence, remains true for lattices given by the cohomology of Lubin-Tate spaces.
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A key ingredient in the Taylor-Wiles proof of Fermat last theorem is the classical Iharas lemma which is used to rise the modularity property between some congruent galoisian representations. In their work on Sato-Tate, Clozel-Harris-Taylor proposed a generalization of the Iharas lemma in higher dimension for some similitude groups. The main aim of this paper is then to prove some new instances of this generalized Iharas lemma by considering some particular non pseudo Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level rising statement.
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