Journal of Lie Theory

no. 4
A Method of Proving Non-Unitarity of Representations of p-adic Groups
Journal of Lie Theory, Volume 22 (2012) no. 4, pp. 1109-1124
The authors study irreducible subquotients of a certain class of induced representations of classical p-adic groups SO(2n+1,F) and Sp(2n,F). The induced representations in question are the ones which contain, as subquotients, generalized Steinberg and generalized trivial representation. We prove that the only unitarizable irreducible subquotients of the induced representations in question are precisely generalized Steinberg and generalized trivial representation, thus continuing the previous work of the first author and M. Tadic. This is, in a certain sense, a generalization of Casselman's results in the case of classical p-adic groups.
DOI: 10.5802/jolt.708
Classification: 22E35, 22E50, 11F70
Keywords: Classical p-adic groups, generalized Steinberg representation, unitary representations, non-unitarity criterion 
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     author = {M. Hanzer and C. Jantzen},
     title = {A {Method} of {Proving} {Non-Unitarity} of {Representations} of p-adic {Groups}},
     journal = {Journal of Lie Theory},
     pages = {1109--1124},
     year = {2012},
     volume = {22},
     number = {4},
     doi = {10.5802/jolt.708},
     zbl = {1259.22009},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.708/}
}
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M. Hanzer; C. Jantzen. A Method of Proving Non-Unitarity of Representations of p-adic Groups. Journal of Lie Theory, Volume 22 (2012) no. 4, pp. 1109-1124. doi: 10.5802/jolt.708

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