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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the arithmetic of weight spaces in the root lattice


Author: Robert W. Deckhart
Journal: Proc. Amer. Math. Soc. 106 (1989), 81-86
MSC: Primary 17B35; Secondary 17B20
MathSciNet review: 967484
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Abstract: Using the notion of $ i$-blocks in a weight space of the positive cone of the root lattice we obtain, after suitable reduction to nontrivial cases, a surprising strongly inductive formula for Kostant's partition function in terms of exactly 3 lower weight spaces. The proof is elementary, using arithmetic properties of $ i$-blocks from [2], and avoiding any character formulas.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0967484-7
PII: S 0002-9939(1989)0967484-7
Article copyright: © Copyright 1989 American Mathematical Society