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...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of algebra Vol. 319; no. 1; pp. 457 - 490
Main Authors:	Cheng, Shun-Jen, Taylor, David G., Wang, Weiqiang
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 2008
Subjects:	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
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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