Geodesic
Classitification of group subschemes in $\operatorname{GL}_n$, that contain a split maximal torus
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 281-296 
E. A. Sopkina. Classitification of group subschemes in $\operatorname{GL}_n$, that contain a split maximal torus. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 281-296. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a16/
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     title = {Classitification of group subschemes in~$\operatorname{GL}_n$, that contain a~split maximal torus},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We describe group subschemes of $\operatorname{GL}_n$ over an arbitrary field, that contain a split maximal torus. This is a joint generalization of the papers by Z. I. Borewicz, G. M. Seitz, N. A. Vavilov and others on description of overgroups of maximal torus and the works by Ch. Wenzel on parabolic subschemes.

[1] Z. I. Borevich, N. A. Vavilov, “Podgruppy polnoi lineinoi gruppy nad polulokalnym koltsom, soderzhaschie gruppu diagonalnykh matrits”, Trudy MIAN SSSR, 148, 1978, 43–57 | MR | Zbl

[2] N. A. Vavilov, “Podgruppy grupp Shevalle, soderzhaschie maksimalnyi tor”, Trudy Len. Mat. Obsch., 1, 1990, 64–109, 245–246 | MR

[3] N. A. Vavilov, “Razlozhenie Bryua podgrupp, soderzhaschikh gruppu diagonalnykh matrits, II”, Zap. nauchn. semin. LOMI, 114, 1982, 50–61 | MR | Zbl

[4] A. Borel, J. Tits, “Groupes réductifs”, Inst. Hautes Études Sci. Publ. Math., 27, 1965, 55–151 | MR

[5] F. Knop, “Homogeneous varieties for semisimple groups of rank one”, Compos. Math., 98 (1995), 77–89 | MR | Zbl

[6] N. Vavilov, “Intermediate Subgroups in Chevalley Groups”, London Math. Soc. Lect. Note Ser., 207, 1993, 233–281 | MR

[7] W. C. Waterhouse, Introduction to affine group schemes, Springer, New York, 1979 | MR

[8] C. Wenzel, “Classification of all parabolic subgroup-schemes of a reductive linear algebraic group over an algebraiclly closed field”, Trans. Amer. Math. Soc., 337 (1993), 211–218 | DOI | MR | Zbl

[9] C. Wenzel, “Rationality of $G/P$ for a nonreduced parabolic subgroup-scheme $P$”, Proc. Amer. Math. Soc., 117 (1993), 899–904 | DOI | MR | Zbl