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Some results on reducibility of parabolic induction for classical groups

Given a (complex, smooth) irreducible representation π of the general linear group over a non-archimedean local field and an irreducible supercuspidal representation σ of a classical group, it is shown that the (normalized) parabolic induction of tensor product of π and σ is reducible if there exists ρ in the supercuspidal support of π such that parabolic induction of tensor product of ρ and σ is reducible. In special cases, an irreducibility criteria for parabolic induction of tensor product of π and σ when the above condition is not satisfied, is given.

classical groups, p-adic fields, parabolic induction, irreducibility

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