Geodesic
A note on exponents vs root heights for complex simple Lie algebras
The electronic journal of combinatorics, Tome 13 (2006)
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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 $\mathfrak{ g}$, the partition formed by the exponents of $\mathfrak{ g}$ is dual to that formed by the numbers of positive roots at each height.
DOI : 10.37236/1160
Mots-clés : Cherednik kernel 
@article{10_37236_1160,
     author = {Sankaran Viswanath},
     title = {A note on exponents vs root heights for complex simple {Lie} algebras},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1160},
     zbl = {1112.05102},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1160/}
}
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Sankaran Viswanath. A note on exponents vs root heights for complex simple Lie algebras. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1160

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