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- (avec D. Ciubotaru) On the reducibility of induced representations for classical p-adic groups and related affine Hecke algebras - - arXiv:1710.06223v1, 19 pages, 2017.

Abstract : Let π be an irreducible smooth complex representation of a general linear p-adic group and let σ be an irreducible complex supercuspidal representation of a (quasi-split) classical p-adic group of a given type. We show that the reducibility of the representation of the appropriate p-adic classical group obtained by (normalized) parabolic induction from π⊗σ does not depend on σ, if the supercuspidal support of π is "separated" from σ. (Here, "separated" means that, for each factor ρ of a representation in the supercuspidal support of π, the representation parabolically induced from ρ⊗σmis irreducible.) This was conjectured by E. Lapid and M. Tadi\'c. (In addition, they proved that this induced representation is always reducible if the supercuspidal support is not "separated".) More generally, we study, for a given set I of inertial orbits of supercuspidal representations of p-adic general linear groups, the category C(I;σ) nof smooth complex finitely generated representations of classical p-adic groups of fixed type, but arbitrary rank, and supercuspidal support given by σ and I, show that this category is equivalent to a category of finitely generated right modules over a direct sum of tensor products of extended affine Hecke algebras of type A, B and D and establish functoriality properties, relating categories with disjoint I's. The proof of the above reducibility result is then based on Hecke algebra arguments, using Kato's exotic geometry.

- On the value on a spherical vector of a standard intertwining operator relative to an everywhere unramified automorphic character - - arXiv:1709.09107v1, 10 pages, 2017.