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A note on exponents vs root heights for complex simple Lie algebras

Sankaran Viswanath
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Abstract

We give an elementary combinatorial proof of a special case of a result due to Bazlov and Ion concerning the Fourier coefficients of the Cherednik kernel. This can be used to give yet another proof of the classical fact that for a complex simple Lie algebra, the partition formed by its exponents is dual to that formed by the numbers of positive roots at each height.

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Sankaran Viswanath. 2006-09-08. A note on exponents vs root heights for complex simple Lie algebras. https://arxiv.org/abs/math/0609248

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