# Cohomology of complements of toric arrangements associated with root systems

Cohomology of complements of toric arrangements associated with root systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

# Cohomology of complements of toric arrangements associated with root systems

, Volume 9 (1) – Mar 1, 2022
17 pages

/lp/springer-journals/cohomology-of-complements-of-toric-arrangements-associated-with-root-rypBVeQPsY
Publisher
Springer Journals
eISSN
2197-9847
DOI
10.1007/s40687-021-00305-z
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Research in the Mathematical SciencesSpringer Journals

Published: Mar 1, 2022

Keywords: Toric arrangements; Root systems; Weyl groups

### References

Access the full text.