Preface 1 1. Classical groups 4 2. Parabolic induction 10 3. Admissible representations 16 4. Jacquet modules and cuspidal representations 24 5. Composition series of induced representations of SL(2, F ) and GL(2, F ) 34 6. Some examples 39 7. Parabolically induced representations of SL(2, F ) and GL(2, F ) 45 8. Some general consequences 52 9. GL(n, F ) 55 10. GSp(n, F ) 62 11. On the reducibi...

Let G be a unitary, symplectic or orthogonal group over a non-archimedean local field of residual characteristic different from 2, considered as the fixed point subgroup in a general linear group G̃ of an involution. Following [7] and [13], we generalize the notion of a semisimple character for G̃ and for G. In particular, following the formalism of [4], we show that these semisimple characters h...