The Bloch–Okounkov correlation functions of negative levels

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 gl ˆ ∞ -modules of...

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Veröffentlicht in:Journal of algebra Jg. 319; H. 1; S. 457 - 490
Hauptverfasser: Cheng, Shun-Jen, Taylor, David G., Wang, Weiqiang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 2008
Schlagworte:
Correlation functions
Infinite-dimensional Lie algebras
q-dimension formulas
Representations at negative levels
Representations at negative levels
Infinite-dimensional Lie algebras
Correlation functions
q-dimension formulas
ISSN:0021-8693, 1090-266X
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Zusammenfassung: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 gl ˆ ∞ -modules of level one. These correlation functions have been generalized for irreducible integrable modules of gl ˆ ∞ 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 gl ˆ ∞ and its classical subalgebras at negative levels.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2007.06.037