  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
$\hat{gl}_\infty$-modules of level one. These correlation functions have been
generalized for irreducible integrable modules of $\hat{gl}_\infty$ 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 $\hat{gl}_\infty$ and its classical
subalgebras at negative levels.
