arXiv:1811.04293 Abstract | arXiv Analytics

arXiv:1811.04293 [math.RT]Abstract References Reviews Resources

Theta lifts of generic representations for dual pairs $(\mathrm{Sp}_{2n}, \mathrm{O}(V))$

Published 2018-11-10Version 1

We determine the occurrence and explicitly describe the theta lifts on all levels of all the irreducible generic representations for the dual pair of groups $(\mathrm{Sp}_{2n}, \mathrm{O}(V))$ defined over a local nonarchimedean field $\mathbb{F}$ of characteristic $0$. As a direct application of our results, we are able to produce a series of non-generic unitarizable representations of these groups.

Categories: math.RT

Subjects: 22E35, 22E50, 11F70

Keywords: theta lifts, dual pair, local nonarchimedean field, irreducible generic representations, direct application

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