On the Non-Vanishing of Poincar\'{e} Series on the Metaplectic Group
classification
🧮 math.RT
math.NT
keywords
metaplecticgroupmathbbmathrmnon-vanishingpoincarseriesadapting
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In this paper, we study the $ K $-finite matrix coefficients of integrable representations of the metaplectic cover of $ \mathrm{SL}_2(\mathbb R) $ and give a result on the non-vanishing of their Poincar\'{e} series. We do this by adapting the techniques developed for $ \mathrm{SL}_2(\mathbb R) $ by Mui\'{c} to the case of the metaplectic group.
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