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JOURNALS // Zapiski Nauchnykh Seminarov POMI

Zap. Nauchn. Sem. POMI, 2011, Volume 386, Pages 203–226 (Mi znsl3912)

Big and small elements in Chevalley groups
N. L. Gordeev, E. W. Ellers

References

1. A. Borel, Linear Algebraic groups, Graduate texts in mathematics, 126, 2nd enl. ed., Springer-Verlag New York Inc., 1991  crossref  mathscinet  zmath
2. N. Bourbaki, Éléments de Mathématique. Groupes et Algèbres de Lie, Chap. IV, V, VI, 2ème édition, Masson, Paris, 1981  mathscinet
3. R. W. Carter, Finite Groups of Lie Type, Conjugacy Classes and Complex Characters, John Wiley & Sons, Chichester et al., 1985  mathscinet  zmath
4. Key Yuen Chan, Jiang-Hua Lu, Simon Kai Ming To, “On intersections of conjugacy classes and Bruhat cells”, Transformation groups, 15:2 (2010), 243–260  crossref  mathscinet  isi
5. E. W. Ellers, N. Gordeev, “Intersection of conjugacy classes with Bruhat cells in Chevalley groups”, Pacific J. Math., 214:2 (2004), 245–261  crossref  mathscinet  zmath  isi
6. E. W. Ellers, N. Gordeev, “Intersection of conjugacy classes with Bruhat cells in Chevalley groups: The cases $\mathrm{SL}_n(K)$, $\mathrm{GL}_n(K)$”, J. Pure and Appl. Algebra, 209 (2007), 703–723  crossref  mathscinet  zmath  isi
7. J. E. Humphreys, Linear Algebraic Groups, Graduate Texts in Mathematics, 21, Springer-Verlag, New York–Heidelberg–Berlin, 1975  crossref  mathscinet  zmath
8. N. Kawanaka, “Unipotent elements and characters of finite Chevalley groups”, Osaka J. Math., 12:2 (1975), 523–554  mathscinet  zmath
9. G. Lusztig, From conjugacy classes in the Weyl Group to unipotent classes, 2010, arXiv: 1003.0412v4
10. G. Lusztig, On $C$-small conjugacy classes in a reductive group, 2010, arXiv: 1005.4313v1  mathscinet
11. J. N. Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lect. Notes Math., 946, Springer-Verlag, Berlin–Heidelberg–New York, 1980  mathscinet
12. T. A. Springer, Linear Algebraic Groups, Progress in Mathematics, 9, 2nd edition, Birkhäuser Boston, Boston, MA, 1998  mathscinet  zmath
13. T. A. Springer, R. Steinberg, “Conjugacy classes”: A. Borel et al, Seminar on Algebraic Groups and Related Finite Groups, Part E, Lect. Notes Math., 131, Springer-Verlag, Berlin–Heidelberg–New York, 1970, 167–266  crossref  mathscinet
14. R. Steinberg, “Regular elements of semisimple algebraic groups”, Inst. Hautes Études Sci. Publ. Math., 25 (1965), 49–80  crossref  mathscinet
15. Vestnik Leningrad Univ. Math., 22:3 (1989), 1–6  mathscinet  zmath
16. N. A. Vavilov, A. A. Semenov, “Bruhat decomposition for long root tori in Chevalley groups”, Zap. Nauchn. Semin. LOMI, 175, 1989, 12–23  mathnet  mathscinet  zmath


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