Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-08T07:44:09.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, II

Published online by Cambridge University Press:  11 January 2016

Toshiaki Shoji
Toshiaki Shoji*
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is concerned with the problem of the determination of unknown scalars involved in the algorithm of computing the generalized Green functions of reductive groups G over a finite field. In the previous paper, we have treated the case where G = SLn. In this paper, we determine the scalars in the case where G is a classical group Sp2n or SON for arbitrary characteristic.

Keywords

20G0520G40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 188 , December 2007 , pp. 133 - 170
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

[D] Dieudonnè, J., La Gèomètrie des Groupes Classiques, Springer-Verlag, 1971.Google Scholar
[L1] Lusztig, G., Intersection cohomology complexes on a reductive group, Invent. Math., 75 (1984), 205–272.CrossRefGoogle Scholar
[L2] Lusztig, G., Character sheaves, I, Adv. in Math., 56 (1985), 193–237, II, Adv. in Math., 57 (1985), 226–265, III, Adv. in Math., 57 (1985), 266–315, IV, Adv. in Math., 59 (1986), 1–63, V, Adv. in Math., 61 (1986), 103–155.CrossRefGoogle Scholar
[LS] Lusztig, G. and Spaltenstein, N., On the generalized Springer correspondence for classical groups, Advanced Studies in Pure Math. Vol. 6 (1985), pp. 289–316.CrossRefGoogle Scholar
[S1] Shoji, T., On the Green polynomials of classical groups, Invent. Math., 74 (1983), 237–267.CrossRefGoogle Scholar
[S2] Shoji, T., Generalized Green functions and unipotent classes for finite reductive groups, I, Nagoya Math. J., 184 (2006), 155–198.Google Scholar
[Sp1] Spaltenstein, N., Classes Unipotentes et Sous-groupes de Borel, Lecture Note in Math. 946, Springer-Verlag, 1982.Google Scholar
[Sp2] Spaltenstein, N., On the generalized Springer correspondence for exceptional groups, Advanced Studies in Pure Math. Vol. 6 (1985), pp. 317–338.CrossRefGoogle Scholar
[SS] Springer, T. A. and Steinberg, R., Conjugacy classes, Seminar on Algebraic Groups and Related Finite Groups, Lect. Note in Math. 131, Springer-Verlag (1970), pp. 167–266.Google Scholar