The paper identifies explicit regions of positive reals that characterize the monoids of totally positive elements for Chevalley groups realized via root categories.
Steinberg.Lectures on Chevalley groups, volume 66 ofUniversity Lecture Series
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Notes on Chevalley Groups and Root Category III: the Region of Total Positivity
The paper identifies explicit regions of positive reals that characterize the monoids of totally positive elements for Chevalley groups realized via root categories.