References
Alvis, D.: Duality in the character ring of a finite Chevalley group. In: Proc. of the Santa Cruz Conference on Finite Groups (Proc. Symp. Pure Math.37) pp. 353–357. Providence: Amer. Math. Soc. 1980
Bourbaki, N.: Groupes et algebres de Lie, Chapter 4, 5, 6., Paris: Hermann 1968
Curtis, C.W.: Truncation and duality in the character ring of a finite group of Lie type. J. of Alg.62, 320–332 (1980)
Deligne, P., Lusztig, G.: Duality for representations of a reductive group over a finite, field. J. of Alg.74, 284–291 (1982)
Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Amer. Math. Soc. Transl. Ser. 2,6, 111–245 (1957)
Elkington, G.B.: Centralizers of unipotent elements in semisimple algebraic groups. J. of Alg.23, 137–163 (1972)
Halmos, P.R., Vaughan, H.E.: The marriage problem. Amer. J. Math.72, 214–215 (1950)
Harish-Chandra: Eisenstein Series over Finite Fields. In: Functional Analysis and Related Fields, pp. 76–88. Berlin- Heidelberg-New York: Springer 1970
Kawanaka, N.: Fourier transforms of nilpotently supported invariant functions on a finite simple Lie algebra. Proc. Japan Acad.57, 461–464 (1981)
Kazhdan, D.A., Proof of Springer's hypothesis. Israel J. Math.28, 272–286 (1977)
Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group.. Amer. J. Math.81, 973–1032 (1959)
Lusztig, G.: Representations of Finite Chevalley Groups. C.B.M.S. Regional Conference Series in Math.39. Amer. Math. Soc. 1978
Lusztig, G., Spaltenstein, N.: Induced unipotent classes. J. London Math. Soc. (2)19, 41–52 (1979)
Rosenlicht, M.: On quotient varieties and the affine embedding of certain homogeneous spaces. Trans. Amer. Math. Soc.101, 211–223 (1961)
Shoji, T.: On the Green polynomials of a Chevalley group of typeF 4. Comm. Algebra10, 505–543 (1982)
Springer, T.A.: The Unipotent Variety of a Semi-simple Group. In: Bombay Colloq. on algebraic geometry, pp. 373–391. London: Oxford University Press 1969
Springer, T.A.: Cusp forms for finite groups. In: Seminar on algebraic groups and related finite groups. Lecture Notes in Mathematics, vol.131, Part C. Berlin-Heidelberg-New York: Springer 1970
Springer, T.A.: Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Invent. Math.36, 173–203 (1976)
Springer, T.A.: The Steinberg function of a finite Lie algebra. Invent. Math.58, 211–223 (1980)
Springer, T.A., Steinberg, R.: Conjugacy classes. In: Seminar on algebraic groups and related finite groups. Lecture Notes in Mathematics. vol.131, Part E. Berlin-Heidelberg-New York: Springer 1970
Steinberg, R.: Lectures on Chevalley groups. Yale University 1967
Steinberg, R.: Endomorphisms of linear algebraic groups. Mem. Amer. Math. Soc. no.80. (1968)
Tits, J.: Buildings of spherical type and finite BN-pairs. Lecture Notes in Mathematics. vol.386. Berlin-Heidelberg-New York: Springer 1974
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This research was supported in part by Grant-in-Aid for Scientific Research, Ministry of Education
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Kawanaka, N. Fourier transforms of nilpotently supported invariant functions on a simple lie algebra over a finite field. Invent Math 69, 411–435 (1982). https://doi.org/10.1007/BF01389363
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DOI: https://doi.org/10.1007/BF01389363