Geometry of microweight tori. (Russian) Zbl 1324.20026

Vavilov, N. A.; Nesterov, V. V.

Vladikavkaz. Mat. Zh. 10, No. 1, 10-23 (2008).

Summary: The authors announce their recent results related to the geometry of microweight and long root tori. A reduction theorem is formulated for the problem of description of subgroups, generated by pairs of tori of these kinds, as well as an existence theorem of a low rank unipotent element in the above subgroups. Before the studies of the authors, these results were known only for the model case of 1-tori in the general linear group [the first author, St. Petersbg. Math. J. 19, No. 3, 407-429 (2008); translation from Algebra Anal. 19, No. 3, 119-150 (2007; Zbl 1202.20054); and A. M. Cohen, H. A. Cuypers, and H. Sterk, Can. J. Math. 51, No. 6, 1149-1174 (1999; Zbl 0952.20042)]. We formulate also open problems in this field.

MSC:

20G15

Linear algebraic groups over arbitrary fields

Keywords:

Chevalley groups; weight elements; microweight tori; long root tori; low rank unipotent elements

Citations:

Zbl 0952.20042; Zbl 1202.20054