The Bloch–Okounkov correlation functions of negative levels

Bloch and Okounkov introduced an n-point correlation function on the fermionic Fock space and found a closed formula in terms of theta functions. This function affords several distinguished interpretations and in particular can be formulated as correlation functions on irreducible -modules of level one. These correlation functions have been generalized for irreducible integrable modules of and its classical Lie subalgebras of positive levels by the authors. In this paper we extend further these results and compute the correlation functions as well as the q-dimensions for modules of and its classical subalgebras at negative levels.