Derived character maps of Lie representations and Chern--Simons forms
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We study the derived representation scheme $ \drep_{\g}(\fra) $ parametrizing the representations of a Lie algebra $ \fra $ in a reductive Lie algebra $ \g $. We define two canonical maps $, \Tr_{\g}(\fra):, \hc_{\bullet}^{(r)}(\fra) \to \h_{\bullet}[\drep_{\g}(\fra)]^G $ and $ \Phi_{\g}(\fra):,\h_{\bullet}[\drep_{\g}(\fra)]^G \to \h_{\bullet}[\drep_{\frh}(\fra)]^{\bW} $, called the Drinfeld trace and the derived Harish-Chandra homomorphism, respectively. The Drinfeld trace is defined on the
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Kassabov, Martin D.