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C. Jantzen has defined a correspondence which attaches to an irreducible representation of a classical $p$-adic group, a finite set of irreducible representations of classical $p$-adic groups supported in a single or in two cuspidal lines (the case of the single cuspidal lines is interesting for the unitarizability). It would be important to know if this correspondence preserves the unitarizability (in both directions). The main aim of this paper is to complete the proof started in the previous paper of the fact that if we have an irreducible unitarizable representation $\pi$ of a classical $p$-adic group whose one attached representation $X_\rho(\pi)$ supported by a cuspidal line, has the same infinitesimal character as the generalized Steinberg representation supported in that line, then $X_\rho(\pi)$ is unitarizable.

Author

Tadic, Marko

Published

2017

Language

EN