Abstract
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 connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, etc., and it can also be interpreted as correlation functions on integrable \(\widehat{{\mathfrak{gl}}}_\infty\) -modules of level one. Such \(\widehat{ {\mathfrak{gl}}}_\infty\) -correlation functions at higher levels were then calculated by Cheng and Wang.
In this paper, generalizing the type A results, we formulate and determine the n-point correlation functions in the sense of Bloch-Okounkov on integrable modules over classical Lie subalgebras of \(\widehat{{\mathfrak{gl}}}_\infty\) of type B, C, D at arbitrary levels. As byproducts, we obtain new q-dimension formulas for integrable modules of type B, C, D and some fermionic type q-identities.
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Communicated by L. Takhtajan
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Taylor, D.G., Wang, W. The Bloch-Okounkov Correlation Functions of Classical Type. Commun. Math. Phys. 276, 473–508 (2007). https://doi.org/10.1007/s00220-007-0344-x
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DOI: https://doi.org/10.1007/s00220-007-0344-x