, Volume 180, Issue 3, pp 315-329
Date: 29 Dec 2011

Big and small elements in Chevalley groups

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Let \( \tilde{G} \) be a reductive algebraic group, which is defined and split over a field K. Here the Zariski open subset \( \mathfrak{B} \) of the group \( \tilde{G} \) that consists of elements such that their conjugacy classes intersect the Big Bruhat Cell is considered. In particular, a description is given for the set \( \mathfrak{B}(K) \) in the case \( \tilde{G} = {\text{G}}{{\text{L}}_n} \) , SL n . Bibliography: 16 titles.

Published in Zapiski Nauchnykh Seminarov POMI, Vol. 386, 2011, pp. 203–226.