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Bruhat decomposition of two-dimensional transforms. (English. Russian original) Zbl 0716.20024

Vestn. Leningr. Univ., Math. 22, No. 3, 1-6 (1989); translation from Vestn. Leningr. Univ., Ser. I 1989, No. 3, 3-7 (1989).
Summary: The purpose of the study is to find a Bruhat decomposition of a two- dimensional transform (i.e., a matrix x such that the rank of the matrix \(x-e=2)\) in a general linear group over a field. This question is relevant for descriptions of subgroups of a special linear group that contain the group of diagonal matrices and certain other related problems. A similar analysis for one-dimensional transforms was performed in the author’s earlier paper [Vestn. Leningr. Univ., Ser. I 1986, No.3, 14-20 (1986; Zbl 0613.20028)].

MSC:

20G15 Linear algebraic groups over arbitrary fields

Citations:

Zbl 0613.20028