| Bloch and Okounkov introduced an n-point correlation function on the infinite wedge space and found an elegant closed formula in terms of theta functions. This function has remarkable connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc. The viewpoint taken here is that it can also be interpreted as a correlation function on integrable gl&d14;infinity -modules of level one. Such gl&d14;infinity -correlation functions at higher levels were then calculated by Cheng and Wang.;In this dissertation, generalizing the above results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of gl&d14;infinity of type B, C, D at arbitrary (positive integral and half-integral) levels. As byproducts, we obtain new q-dimension formulas for these modules of type B, C, D and fermionic type q-identities. We also formulate and compute the correlation functions and q-dimension formulas of highest weight modules of these classical Lie algebras of types A, C, D at negative integral and half-integral levels. |
