Proceedings of the Japan Academy, Series A, Mathematical Sciences

Fourier transforms of nilpotently supported invariant functions on a finite simple Lie algebra

Noriaki Kawanaka

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 57, Number 9 (1981), 461-464.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
http://projecteuclid.org/euclid.pja/1195516260

Mathematical Reviews number (MathSciNet)
MR637555

Zentralblatt MATH identifier
0503.20016

Digital Object Identifier
doi:10.3792/pjaa.57.461

Subjects
Primary: 17B15: Representations, analytic theory

Citation

Kawanaka, Noriaki. Fourier transforms of nilpotently supported invariant functions on a finite simple Lie algebra. Proceedings of the Japan Academy, Series A, Mathematical Sciences 57 (1981), no. 9, 461--464. doi:10.3792/pjaa.57.461. http://projecteuclid.org/euclid.pja/1195516260.


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References

  • [1] D. Alvis: Duality in the character ring of a finite Chevalley group. Proc. of the Santa Cruz Conference Finite groups (Proc. Symp. Pure Math., 37), Amer. Math. Soc, Providence, pp. 353-357 (1980).
  • [2] C. W. Curtis: Truncation and duality in the character ring of a finite group of Lie type, J. of Alg., 62, 320-332 (1980).
  • [3] P. Deligne and G. Lusztig: Duality for representations of a reductive groups over a finite field (to appear).
  • [4] E. B. Dynkin: Semisimple subalgebras of semisimple Lie algebras. Amer. Math. Soc. Transl., ser. 2, 6, 111-245 (1957).
  • [5] N. Kawanaka: Unipotent elements and characters of finite Chevalley groups. Osaka J. Math., 12, 523-554 (1975).
  • [6] B. Kostant: The principal three dimensional subgroup and the Betti numbers of a complex simple Lie group. Amer. J. Math., 81, 973-1032 (1959).
  • [7] T. A. Springer: Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Invent, math., 38, 173-203 (1976).
  • [8] T. A. Springer: The Steinberg function of a finite Lie algebra, ibid., 58, 211-215 (1980).
  • [9] T. A. Springer and R. Steinberg: Conjugacy classes. Seminar on Algebraic Groups and Related Finite Groups. Lect. Notes in Math., vol. 131, part E, Springer, Berlin-Heidelberg-New York (1970).