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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Vydáno v:Journal of algebra Ročník 319; číslo 1; s. 457 - 490
Hlavní autoři: Cheng, Shun-Jen, Taylor, David G., Wang, Weiqiang
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 2008
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ISSN:0021-8693, 1090-266X
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Abstract 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.
AbstractList 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.
Author Taylor, David G.
Cheng, Shun-Jen
Wang, Weiqiang
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  givenname: David G.
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  givenname: Weiqiang
  surname: Wang
  fullname: Wang, Weiqiang
  email: ww9c@virginia.edu
  organization: Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA
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Issue 1
Keywords Representations at negative levels
Infinite-dimensional Lie algebras
Correlation functions
q-dimension formulas
Language English
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Snippet 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...
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SubjectTerms Correlation functions
Infinite-dimensional Lie algebras
q-dimension formulas
Representations at negative levels
Title The Bloch–Okounkov correlation functions of negative levels
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