Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields II

References

• Bala, P., Carter, R. (1976). Classes of unipotent elements in simple algebraic groups I. Math. Proc. Cambridge Philos. Soc. 79:401–425.
   Web of Science ®Google Scholar
• Bala, P., Carter, R. (1976). Classes of unipotent elements in simple algebraic groups II. Math. Proc. Cambridge Philos. Soc. 80:95–104.
   Web of Science ®Google Scholar
• Bate, M., Herpel, S., Martin, B., Röhrle, G. (2016). Cocharacter-closure and the rational Hilbert-Mumford theorem. Math. Z. doi:10.1007/s00209-016-1816-5.
   Google Scholar
• Bate, M., Herpel, S., Martin, B., Röhrle, G. (2015). G-complete reducibility in non-connected groups. Proc. Am. Math. Soc. 143:1085–1100.
   Web of Science ®Google Scholar
• Bate, M., Martin, B., Röhrle, G. (2005). A geometric approach to complete reducibility. Invent. Math. 161:177–218.
   Web of Science ®Google Scholar
• Bate, M., Martin, B., Röhrle, G. (2010). Complete reducibility and separable field extensions. C. R. Acad. Sci. Paris 348:495–497.
   Web of Science ®Google Scholar
• Bate, M., Martin, B., Röhrle, G., Tange, R. (2010). Complete reducibility and separability. Trans. Am. Math. Soc. 362(8):4283–4311.
   Web of Science ®Google Scholar
• Bate, M., Martin, B., Röhrle, G., Tange, R. (2013). Closed orbits and uniform S-instability in geometric invariant theory. Trans. Am. Math. Soc. 365(7):3643–3673.
   Web of Science ®Google Scholar
• Borel, A. (1991). Linear Algebraic Groups. Graduate Texts in Mathematics, 2nd ed. New York: Springer.
   Google Scholar
• Borel, A., Tits, J. (1965). Groupes réductifs. Publ. Math. IHES 27:55–150.
   Google Scholar
• Carter, R. (1972). Simple Groups of Lie Type. John Wiley & Sons.
   Google Scholar
• Conrad, B., Gabber, O., Prasad, G. (2010). Pseudo-reductive Groups. Cambridge.
   Google Scholar
• Gille, P. (2002). Unipotent subgroups of reductive groups in characteristic p>0. Duke Math. 114(2):307–328.
   Web of Science ®Google Scholar
• Gille, P. (2013). Exemples de groupes semi-simples simplement connexes anisotropes contenant un sous-groupe unipotent. Quart. J. Math. 9(3):487–492.
   Google Scholar
• Leeb, B., Ramos-Cuevas, C. (2011). The centre conjecture for spherical buildings of types F4 and E6. Geom. Funct. Anal. 21(3):525–559.
   Web of Science ®Google Scholar
• Lidl, R., Niederreiter, H. (1986). Introduction to Finite Fields and their Applications. Cambridge University Press.
   Google Scholar
• Liebeck, M., Martin, B., Shalev, A. (2005). On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function. Duke Math. J. 128(3):541–557.
   Web of Science ®Google Scholar
• Liebeck, M., Seitz, G. (1996). Reductive subgroups of exceptional algebraic groups. Mem. Am. Math. Soc. 121:580.
   Google Scholar
• Liebeck, M., Seitz, G. (2003). Variations on a theme of Steinberg. Special issue celebrating the 80th birthday of Robert Steinberg. J. Algebra 260(1):261–297.
   Web of Science ®Google Scholar
• Liebeck, M., Seitz, G. (2010). Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras. AMS Math. Surveys and Monographs, Vol. 180.
   Google Scholar
• Liebeck, M., Testerman, D. (2004). Irreducible subgroups of algebraic groups. Q. J. Math. 55:47–55.
   Web of Science ®Google Scholar
• Lusztig, G. (1976). On the finiteness of the number of unipotent classes. Invent. Math. 34:201–214.
   Web of Science ®Google Scholar
• Mühlherr, B., Tits, J. (2006). The centre conjecture for non-exceptional buildings. J. Algebra 300(2):687–706.
   Web of Science ®Google Scholar
• Nagata, M. (1961). Complete reducibility of rational representations of a matric group. J. Math. Kyoto Univ. 1:87–99.
   Google Scholar
• Ramos-Cuevas, C. (2012). The center conjecture for thick spherical buildings. Geom. Dedicata 166:349–407.
   Web of Science ®Google Scholar
• Richardson, R. (1982). On orbits of algebraic groups and Lie groups. Bull. Austral. Math. Soc. 25(1):1–28.
   Web of Science ®Google Scholar
• Richardson, R. (1988). Conjugacy classes of n-tuples in Lie algebras and algebraic groups. Duke Math. J. 57:1–35.
   Web of Science ®Google Scholar
• Serre, J. (2005). Complète Réductibilité. Séminaire Bourbaki. Astérisque 299:195–217 (Vol. 2003/2004).
   Google Scholar
• Springer, T. (1998). Linear Algebraic Groups. Progress in Mathematics, 2nd ed. Boston: Birkhäuser.
   Google Scholar
• Springer, T., Steinberg, R. (1970). Conjugacy classes. In: Seminar on Algebraic Groups and Related Topics. Lecture Notes in Mathematics, Vol. 131. Berlin, Heidelberg: Springer.
   Google Scholar
• Stewart, D. (2014). Non-G-completely reducible subgroups of the exceptional groups. Int. Math. Res. Not. 2014(22):6053–6078.
   Google Scholar
• Tits, J. (1962). Groupes Semi-simples Isotropes. Colloq. Théorie des Groupes Algébriques, Bruxelles. Louvain, Librairie Universitaire; Paris, Gauthier-Villars.
   Google Scholar
• Tits, J. (1974). Buildings of Spherical Type and Finite BN-pairs. Lecture Notes in Mathematics, Vol. 386, 1st ed. Berlin, Heidelberg: Springer.
   Google Scholar
• Tits, J. (1986). Unipotent elements and parabolic subgroups of reductive groups II. Lecture Notes in Mathematics. Algebraic Groups (Utrecht, Netherlands). Berlin: Springer, Vol. 1271, pp. 33–62.
   Google Scholar
• Tits, J. (1992/93). Théorie des groupes. Ann. Collège France 93:113–131.
   Google Scholar
• Uchiyama, T. (2017). Non-separability and complete reducibility: E_n examples with an application to a question of Külshammer. Journal of Group Theory. https://doi.org/10.1515/jgth-2017-0005
   Google Scholar
• Uchiyama, T. (2015). Separability and complete reducibility of subgroups of the Weyl group of a simple algebraic group of type E7. J. Algebra 422:357–372.
   Web of Science ®Google Scholar
• Uchiyama, T. (2016). Complete reducibility of subgroups of reductive algebraic groups over nonperfect fields I. J. Algebra 463:168–187.
   Web of Science ®Google Scholar