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arXiv · 1807.08605

Shadows in Coxeter groups

Marius Graeber·Petra Schwer
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Abstract

For a given $w$ in a Coxeter group $W$ the elements $u$ smaller than $w$ in Bruhat order can be seen as the end-alcoves of stammering galleries of type $w$ in the Coxeter complex $\Sigma$. We generalize this notion and consider sets of end-alcoves of galleries that are positively folded with respect to certain orientation $\phi$ of $\Sigma$. We call these sets shadows. Positively folded galleries are closely related to the geometric study of affine Deligne-Lusztig varieties, MV polytopes, Hall-Littlewood polynomials and many more agebraic structures. In this paper we will introduce various notions of orientations and hence shadows and study some of their algorithmic properties.

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BibTeXRIS

Marius Graeber, Petra Schwer. 2018-07-23. Shadows in Coxeter groups. https://doi.org/10.1007/s00026-019-00485-0

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