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Weight Spaces and Root Spaces of Kac-Moody Algebras

Zhu, Y. C. (1994) Weight Spaces and Root Spaces of Kac-Moody Algebras. Journal of Algebra, 168 (3). pp. 936-948. ISSN 0021-8693. https://resolver.caltech.edu/CaltechAUTHORS:20170906-105926985

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Abstract

Let g(A) be the Kac-Moody algebra associated to a generalized symmetric Cartan matrix A, and g(A) = n_⊕ h ⊕ n_+ be its triangular decomposition. The purpose of this paper is to give an explicit realization of the weight spaces of an integrable highest weight module of g(A) and the weight spaces of the universal enveloping algebra U(n_) in terms of certain function spaces. We also discuss a similar construction for the root spaces. Our approach is based on a vertex operator construction of Kac-Moody algebras and representations by Borcherds [Bo} and uses the results on matrix coefficient of vertex operators given by Frenkel et al. [FLM). We state here our main results for the rank two Kac-Moody algebras; see Theorems 4.1 and 4.2 for the general case.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jabr.1994.1263DOIArticle
http://www.sciencedirect.com/science/article/pii/S0021869384712634PublisherArticle
Additional Information:© 1994 Academic Press. The author thanks Igor Frenkel for discussions and the referee for many helpful suggestions.
Issue or Number:3
Record Number:CaltechAUTHORS:20170906-105926985
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170906-105926985
Official Citation:Y.C. Zhu, Weight Spaces and Root Spaces of Kac-Moody Algebras, Journal of Algebra, Volume 168, Issue 3, 1994, Pages 936-948, ISSN 0021-8693, http://dx.doi.org/10.1006/jabr.1994.1263. (http://www.sciencedirect.com/science/article/pii/S0021869384712634)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81187
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2017 21:28
Last Modified:03 Oct 2019 18:39

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