engleski

On regular square integrable representations of p-adic groups

The paper studies the problem of construction of non-cuspidal irreducible square integrable representations of classical p-adic groups, and questions related to it. Starting from cuspidal reducibilities in the generalized rank one case, we give a construction of regular irreducible square integrable representations of p-adic GSp(n), Sp(n) and SO(2n+1). Under an assumption (which is expected to hold in general), we show that all regular irreducible square integrable representations of Sp(n) and SO(2n+1) should appear in this way. We obtain a number of general results about places where irreducible square integrable representations can appear in parabolically induced representation.We show that among irreducible cuspidal representations of general linear groups, only the self-contragredient ones play role in the construction of square integrable representations of GSp(n), Sp(n) and SO(2n+1). At the end, our regular irreducible square integrable representations are used to show that some basic properties of Whittaker models related to the Langlands classification, are quite different in the case of GL(n) and the other classical groups. We show that for other classical groups there are non-degenerate standard modules with degenerate irreducible subrepresentations.

symplectic groups; orthogonal groups; square integrable representations; Jacquet modules; standard moduls; Whittaker models

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