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Some amazing properties of spherical nilpotent orbits

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References

  1. Adams, J., Huang, J.-S., Vogan, D.: Functions on the model orbit in E8. Representation Theory (electronic) 2, 224–263 (1998)

    Google Scholar 

  2. Brion, M.: Représentations exceptionnelles des groupes semi-simples. Ann. Sci. Éc. Norm. Supér., IV Sér. 18, 345–387 (1985)

    Google Scholar 

  3. Broer, A.: Decomposition varieties in semisimple Lie algebras. Canad. J. Math. 50, 929–971 (1998)

    MathSciNet  MATH  Google Scholar 

  4. Collingwood, D.H., McGovern, W.: Nilpotent orbits in semisimple Lie algebras. New York: Van Nostrand Reinhold, 1993

  5. Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Matem. Sbornik 30 2, 349–462 (1952) (Russian); English translation: Am. Math. Soc. Transl. II Ser. 6, 111–244 (1957)

    MATH  Google Scholar 

  6. Hesselink, W.: The normality of closures of orbits in a Lie algebra. Comment. Math. Helv. 54, 105–110 (1979)

    MathSciNet  MATH  Google Scholar 

  7. Joseph, A.: The minimal orbit in a simple Lie algebra and its associated maximal ideal. Ann. Scient. Éc. Norm. Sup. 9, 1–30 (1976)

    Google Scholar 

  8. Kac, V.G.: Some remarks on nilpotent orbits. J. Algebra 64, 190–213 (1980)

    MathSciNet  MATH  Google Scholar 

  9. Kostant, B.: Lie group representations in polynomial rings. Am. J. Math. 85, 327–404 (1963)

    MATH  Google Scholar 

  10. Luna, D.: Adhérence d’orbite et invariants. Invent. Math. 29, 231–238 (1975)

    MATH  Google Scholar 

  11. Lusztig, G., Spaltenstein, N.: Induced unipotent classes. J. London Math. Soc. 19, 41–52 (1979)

    MathSciNet  MATH  Google Scholar 

  12. McGovern, W.: Rings of regular functions on nilpotent orbits and their covers. Invent. Math. 97, 209–217 (1989)

    MathSciNet  MATH  Google Scholar 

  13. Nervi, J.: Algèbres de Lie simples graduées par un système de racines et sous-algèbres C-admissibles. J. Algebra 223, 307–343 (2000)

    MathSciNet  MATH  Google Scholar 

  14. Panyushev, D.: Complexity and nilpotent orbits. Manuscripta Math. 83, 223–237 (1994)

    MathSciNet  MATH  Google Scholar 

  15. Panyushev, D.: Parabolic subgroups with Abelian unipotent radical as a testing site for Invariant Theory. Canad. J. Math. 51, 616–635 (1999)

    MathSciNet  MATH  Google Scholar 

  16. Panyushev, D.: On spherical nilpotent orbits and beyond. Annales l’Institut Fourier 49, 1453–1476 (1999)

    MathSciNet  MATH  Google Scholar 

  17. Panyushev, D.: Complexity and rank of actions in invariant theory. J. Math. Sci. (New York) 95, 1925–1985 (1999)

    MathSciNet  MATH  Google Scholar 

  18. Panyushev, D.: The index of a Lie algebra, the centralizer of a nilpotent element, and the normalizer of the centralizer. Math. Proc. Camb. Phil. Soc. 134, 41–59 (2003)

    MathSciNet  Google Scholar 

  19. Röhrle, G.: On extraspecial parabolic subgroups. In: Linear algebraic groups and their representations R. Elman et al., (eds.), Contemp. Math. 153, AMS, Providence, 1993, pp. 143–155

  20. Shmelkin, D.: On spherical representations of quivers and generalized complexes. Transformation Groups 7, 87–106 (2002)

    MathSciNet  MATH  Google Scholar 

  21. Springer, T.A., Steinberg, R.: Conjugacy Classes. In: Seminar on algebraic and related finite groups. Lecture Notes Math. Springer-Verlag 131, 1970, pp. 167–266

    Google Scholar 

  22. Vinberg, E.B.: The Weyl group of a graded Lie algebra. Izv. Akad. Nauk SSSR, Ser. Mat. 40, 488–526 (1976) (Russian); English translation: Math USSR-Izv. 10, 463–495 (1976)

    Google Scholar 

  23. Vinberg, E.B., Onishchik, A.L.: Seminar on Lie groups and algebraic groups. Moskva: Nauka 1988 (Russian). English translation: A.L. Onishchik and E.B. Vinberg. Lie groups and algebraic groups. Berlin Heidelberg New York: Springer 1990

  24. Vinberg, E.B., Popov, V.L.: On a class of quasihomogeneous affine varieties. Izv. AN SSSR. Ser. Matem. 36, 749–764 (1972) (Russian); English translation: Math. USSR Izv. 6, 743–758 (1972)

    MATH  Google Scholar 

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  1. Independent University of Moscow, Bol’shoi Vlasevskii per. 11, 121002, Moscow, Russia

    Dmitri I. Panyushev

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  1. Dmitri I. Panyushev
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Panyushev, D. Some amazing properties of spherical nilpotent orbits. Math. Z. 245, 557–580 (2003). https://doi.org/10.1007/s00209-003-0555-6

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