The Bloch-Okounkov correlation functions of negative levels

Cheng, Shun-Jen; Taylor, David G.; Wang, Weiqiang

The Bloch-Okounkov correlation functions of negative levels

Authors

Cheng, Shun-Jen

Taylor, David G.

Wang, Weiqiang

Description

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.
LaTeX, 34 pages, to appear in Journal of Algebra