Abstract
For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced from a cuspidal type. We also give a fundamental step towards the classification of cuspidal representations, identifying when certain cuspidal types induce to equivalent representations; this result is new even in the case of complex representations. Finally, we prove that the representations induced from more general types are quasi-projective, a crucial tool for extending the results here to arbitrary irreducible representations.
Funding source: Engineering and Physical Sciences Research Council
Award Identifier / Grant number: EP/H00534X/1
Funding statement: This work was supported by the Engineering and Physical Sciences Research Council (EP/H00534X/1).
Acknowledgements
We thank the referees for their very careful reading, corrections and useful expositional suggestions which have greatly improved the paper.
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