Abstract
Let \( \mathfrak{g} \) be a complex semisimple Lie algebra. Although the quantum group \( {U}_{\hslash \mathfrak{g}} \) is known to be isomorphic, as an algebra, to the undeformed enveloping algebra \( U\mathfrak{g}\left\llbracket \hslash \right\rrbracket \), no such isomorphism is known when \( \mathfrak{g}\ne \mathfrak{s}{\mathfrak{l}}_2 \). In this paper, we construct an explicit isomorphism for \( \mathfrak{g}=\mathfrak{s}{\mathfrak{l}}_n \), for every n ≥ 2, which preserves the standard flag of type A. We conjecture that this isomorphism quantizes the Poisson diffeomorphism of Alekseev and Meinrenken [2].
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APPEL, A., GAUTAM, S. AN EXPLICIT ISOMORPHISM BETWEEN QUANTUM AND CLASSICAL \( \mathfrak{s}{\mathfrak{l}}_n \). Transformation Groups 25, 945–980 (2020). https://doi.org/10.1007/s00031-019-09543-6
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DOI: https://doi.org/10.1007/s00031-019-09543-6