The Bloch–Okounkov correlation functions of negative levels

Abstract

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 gl ˆ ∞ -modules of level one. These correlation functions have been generalized for irreducible integrable modules of gl ˆ ∞ 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 gl ˆ ∞ and its classical subalgebras at negative levels.