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

Mathematics – Combinatorics

Scientific paper

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5 pages

Scientific paper

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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