The Bloch-Okounkov correlation functions at higher levels

Abstract

We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of ${\widehat{gl}}_{\infty }$ 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