SQUARE INTEGRABLE REPRESENTATIONS OF CLASSICAL p-ADIC GROUPS CORRESPONDING TO SEGMENTS
نویسنده
چکیده
Let Sn be either the group Sp(n) or SO(2n+1) over a p-adic field F . Then Levi factors of maximal parabolic subgroups are (isomorphic to) direct products of GL(k) and Sn−k , with 1 ≤ k ≤ n. The square integrable representations which we define and study in this paper (and prove their square integrability), are subquotients of reducible representations Indn P (δ⊗σ), where δ is an essentially square integrable representation of GL(k), and σ is a cuspidal representation of Sn−k. These square integrable representations play an important role in a construction of more general square integrable representations.
منابع مشابه
On Classification of Some Classes of Irreducible Representations of Classical Groups
Introduction 2 1. Harmonic analysis and unitary duals 2 2. Non-discrete locally compact fields, classical groups, reductive groups 4 3. K0-finite vectors 7 4. Smooth representations 8 5. Parabolically induced representations 9 6. Jacquet modules 12 7. Filtrations of Jacquet modules 14 8. Square integrable and tempered representations 15 9. Langlands classification 16 10. Geometric lemma and alg...
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