On the arithmetic of weight spaces in the root lattice

Deckhart, Robert W.

doi:10.1090/S0002-9939-1989-0967484-7

On the arithmetic of weight spaces in the root lattice
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Proc. Amer. Math. Soc. 106 (1989), 81-86 Request permission

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.

References

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