Geodesic
Big and small elements in Chevalley groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 20, Tome 386 (2011), pp. 203-226

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Let $\widetilde G$ be a reductive algebraic group which is defined and split over a field $K$. Here we consider the Zariski open subset $\mathfrak B$ of the group $\widetilde G$ which consists of elements such that their conjugacy classes intersect the Big Bruhat Cell. In particular, we give a description of the set $\mathfrak B(K)$ in the case $\widetilde G=\mathrm{GL}_n,\mathrm{SL}_n$. Bibl. 16 titles. 
@article{ZNSL_2011_386_a4,
     author = {N. L. Gordeev and E. W. Ellers},
     title = {Big and small elements in {Chevalley} groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {203--226},
     publisher = {mathdoc},
     volume = {386},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_386_a4/}
}
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N. L. Gordeev; E. W. Ellers. Big and small elements in Chevalley groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 20, Tome 386 (2011), pp. 203-226. http://geodesic.mathdoc.fr/item/ZNSL_2011_386_a4/