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arXiv · 2408.09009

Reduced words for reflections in Weyl groups

Elizabeth Milićević
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Abstract

The reflections in a Coxeter group are defined as conjugates of a single generator, and thus admit palindromic expressions as products of generators. Our main result gives closed formulas providing a palindromic reduced expression for each reflection in any finite Weyl group. There exist algorithmic methods for determining such reduced expressions, but explicit formulas have not been recorded outside of well-known special cases.

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Elizabeth Milićević. 2025-04-06. Reduced words for reflections in Weyl groups. https://arxiv.org/abs/2408.09009

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