The Bloch-Okounkov correlation functions at higher levels

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We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of $\hat{gl}_\infty$ and $W_{1+\infty}$ of arbitrary positive integral levels.
Latex, 12 pages. Missing powers of the product $t_1 \cdot t_n$ are inserted in various places. Typos corrected

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