TL;DR
This paper investigates Weyl elements in isotropic reductive groups over rings, providing explicit formulas for their squares, classifying them in rank one cases, and exploring their properties.
Contribution
It introduces an explicit formula for squares of Weyl elements and classifies these elements in rank one groups, advancing understanding of their structure.
Findings
Derived an explicit formula for squares of Weyl elements.
Classified Weyl elements in rank one groups.
Established basic properties of Weyl element loci.
Abstract
We study Weyl elements in isotropic reductive groups over commutative rings. Our main result in an explicit formula for squares of such elements. We also classify these elements in rank one groups and prove basic properties of their loci.
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