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We develop an algorithm for computing the cohomology of complements of toric arrangements. In the case a finite group Γ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Gamma $$\end{document} is acting on the arrangement, the algorithm determines the cohomology groups as representations of Γ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Gamma $$\end{document}. As an important application, we determine the cohomology groups of the complements of the toric arrangements associated with root systems of exceptional type as representations of the corresponding Weyl groups.
Research in the Mathematical Sciences – Springer Journals
Published: Mar 1, 2022
Keywords: Toric arrangements; Root systems; Weyl groups
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