Abstract
In this article, we compute the center of the infinitesimal Hecke algebras H z associated to 𝔰𝔩2; then using nontriviality of the center, we study representations of these algebras in the framework of the BGG category 𝒪. We also discuss central elements in infinitesimal Hecke algebras over 𝔤𝔩 n and 𝔰𝔭(2n) for all n. We end by proving an analogue of Duflo's theorem for H z .
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