This paper presents an explicit mapping between the SU(2)-Reshetikhin-Turaev TQFT vector spaces V-r(Sigma) of surfaces and spaces of holomorphic sections of complex line bundles on some KShler manifold, following the approach of geometric quantization. We explain how curve operators in TQFT correspond to Toeplitz operators with symbols some trace functions. As an application, we show that eigenvectors of these operators are concentrated near the level sets of these trace functions, and obtain asymptotic estimates of pairings of such eigenvectors. This yields under some genericity assumptions an asymptotic for the matrix coefficients of quantum representations.
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