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$\newcommand{\sl}{\mathfrak{sl}}\DeclareMathOperator\SL{SL}$Let $U_h(\sl_2)$ be the quantized universal enveloping algebra of $\sl_2(\mathbb{C})$ and $F_h(\SL_2)$ be the quantized function algebra of $\SL(2, \mathbb{C})$. Theorem 7.1.4 in the book “A Guide to Quantum Groups” by V. Chari and A. N. Pressley shows that the finite dual of $U_h(\sl_2)$ is isomorphic to $F_h(\SL_2)$.

Question The dual of elements $E$, $F$, and $H$ of $U_h(\sl_2)$ corresponds to which element of $F_h(\SL_2)$ by isomorphism?

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