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 algebraic structures 21 11. Square integrable representations of p-adic general linear groups 24 12. Two simple examples of square integrable representations of p-adic classical groups 25 13. Invariants of square integrable representations of classical p-adic groups 27 14. Reduction to cuspidal lines 33 15. Parameters of D(ρ;σ) 35 16. Integral case 36 17. Non-integral case 38 18. Local Langlands correspondences 40 19. Non-unitary duals of classical p-adic groups 42 20. Unitary duals of general linear groups over local fields 43 21. On the unitarizability problem for classical p-adic groups 49 References 53