
Journal of Lie Theory 32 (2022), No. 3, 839862 Copyright Heldermann Verlag 2022 Quantum Duality Principle for Quantum Continuous KacMoody Algebras Fabio Gavarini Department of Mathematics, University of Rome "Tor Vergata", Rome, Italy gavarini@mat.uniroma2.it [Abstractpdf] \newcommand{\uhgx}{U_\hbar(\,\g_X)} \newcommand{\kh}{{\Bbbk[[\hbar]]}} \newcommand{\kqqm}{{\Bbbk\big[\,q\,,q^{1}\big]}} \newcommand {\g}{\mathfrak{g}} For the quantized universal enveloping algebra $\uhgx$ associated with a continuous KacMoody algebra $\g_X$ as in [A.\ Appel, F.\ Sala, \emph{Quantization of continuum {K}ac{M}oody algebras}, Pure Appl.\ Math.\ Q.\ \textbf{16} (2020), 439493], we prove that a suitable formulation of the \textsl{Quantum Duality Principle\/} holds true, both in a ``formal'' version  i.e., applying to the original definition of $\uhgx$ as a \textsl{formal\/} QUEA over $\kh$  and in a ``polynomial'' one  i.e., for a suitable polynomial form of $\uhgx$ over $\kqqm$. In both cases, the QDP states that a suitable Hopf subalgebra of the given quantization of the Lie bialgebra $\g_X$ is in fact a suitable quantization (in formal or in polynomial sense) of a connected Poisson group $G_X^*$ dual to $\g_X$. Keywords: Continuous KacMoody algebras, continuous quantum groups, quantization of Lie bialgebras, quantization of Poisson groups. MSC: 17B37, 20G42; 17B65, 17B62. [ Fulltextpdf (230 KB)] for subscribers only. 