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arXiv · 2306.04514

Grading of affine Weyl semi-groups of Kac-Moody type

Paul Philippe
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Abstract

For any Kac-Moody root data $\mathcal D$, D. Muthiah and D. Orr have defined a partial order on the semi-direct product $W^+$ of the integral Tits cone with the vectorial Weyl group of $\mathcal D$, and a strictly compatible $\mathbb Z$-valued length function. We classify covers for this order and show that this length function defines a $\mathbb Z$-grading of $W^+$, generalizing the case of affine ADE root systems and giving a positive answer to a conjecture of Muthiah and Orr.

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BibTeXRIS

Paul Philippe. 2023-06-07. Grading of affine Weyl semi-groups of Kac-Moody type. https://doi.org/10.2140/pjm.2024.332.273

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