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Weight multiplicity polynomials for affne Kac-Moody algebras of type $A_n^{(1)}

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Authors
Benkart, Georgia; Kang, Seok-Jin; Misra, Kailash C.
Issue Date
1996-11
Publisher
Springer Verlag
Citation
Compositio Math. 104 (1996) 153-187
Keywords
Affine Kac--Moody Lie algebrasweight multiplicityKostka numbers
Abstract
For the affine Kac--Moody algebras X_r^{(1)} it has been conjectured by Benkart and Kass that for fixe d dominant weights \lambda,\mu, the multiplicity of the weight \mu in the irreducible X_r^{(1)}-module L(\lambda) of highest wei ght \lambda is a polynomial in r which depends on the type X of the alg ebra. In this paper we provide a precise conjecture for the degree of that polynomial for the algebras A_r^{(1)}. To offer evidence for this conjecture we p rove it for all dominant weights \lambda and all weights \mu of depth \leqslant 2 by explicitly exhibiting the polynomials as expressions involving Kostka numbers.
ISSN
0010-437X (Print)
1570-5846 (Online)
Language
English
URI
http://hdl.handle.net/10371/12168

http://www.numdam.org/item?id=CM_1996__104_2_153_0
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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