%0 Journal Article
%T The Bloch-Okounkov correlation functions of negative levels
%A Shun-Jen Cheng
%A David G. Taylor
%A Weiqiang Wang
%J Mathematics
%D 2007
%I arXiv
%X 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.
%U http://arxiv.org/abs/0706.3742v1