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Antichains of positive roots and Heaviside functions

Frederic Chapoton
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Abstract

The ring of locally-constant integer-valued functions on the dominant chamber of the Shi arrangement is endowed with a filtration and a new basis, compatible with this filtration, is found. This basis is compared to the trivial basis. The ring is given a presentation by generators and relations.

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Frederic Chapoton. 2003-03-18. Antichains of positive roots and Heaviside functions. https://arxiv.org/abs/math/0303220

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