The Bloch-Okounkov correlation functions of negative levels

Details The Bloch-Okounkov correlation functions of negative levels The Bloch-Okounkov correlation functions of negative levels

2007-06-26

arxiv.org/abs/0706.3742v1

J. Algebra 319 (2008), 457--490.

Mathematics

Representation Theory

LaTeX, 34 pages, to appear in Journal of Algebra

Scientific paper

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.

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