Abstract
Let \(({\rm G, G'}) \subset {\rm Sp}({\rm W})\) be an irreducible real reductive dual pair of type I in stable range, with G the smaller member. In this note, we prove that all irreducible genuine representations of \(\tilde{\rm G}\) occur in the Howe correspondence. The proof uses structural information about the groups forming a reductive dual pair and estimates of matrix coefficients.
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Protsak, V., Przebinda, T. On the occurrence of admissible representations in the real Howe correspondence in stable range. manuscripta math. 126, 135–141 (2008). https://doi.org/10.1007/s00229-007-0161-8
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DOI: https://doi.org/10.1007/s00229-007-0161-8