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Polynomial behavior of weight multiplicities for the affine Kac-Moody algebras $A_n^{(1)}$

Cited 2 time in Web of Science Cited 2 time in Scopus
Authors
Benkart, Georgia; Kang, Seok-Jin; Lee, Hyeonmi; Misra, Kailash C.; Shin, Dong-Uy
Issue Date
2001
Publisher
Cambridge University Press
Citation
Compositio Math. 126 (2001), 91-111
Keywords
Polynomial behaviorWeight Multiplicitiesaffine Kac-Moody algebras
Abstract
We prove that the multiplicity of an arbitrary dominant weight for an integrable highest weight representation of the affine Kac-Moody algebra $A_{r}^{(1)}$ is a polynomial in the rank $r$. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks.
ISSN
0010-437X (Print)
1570-5846 (Online)
Language
English
URI
https://hdl.handle.net/10371/12196
DOI
https://doi.org/10.1023/A:1017584131106
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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