Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T14:02:11.438Z Has data issue: false hasContentIssue false
  • English
  • Français

Some combinatorial results for Weyl groups

Published online by Cambridge University Press:  24 October 2008

A. J. Idowu  and
A. O. Morris
A. J. Idowu
Affiliation:
Department of Mathematics, University of Sokoto, Nigeria
A. O. Morris
Affiliation:
Department of Pure Mathematics, The University College of Wales, Aberystwyth, Dyfed S Y23 3BZ
Get access Rights & Permissions [Opens in a new window]

Extract

The aim of this paper is to prove some results involving Weyl groups which are useful in an application to give a combinatorial construction of representations of Weyl groups which generalizes the well-known Young tableau method for symmetric groups. A preliminary version of these applications has been given in [12]. As these results seem to be of independent interest they are gathered together in the present paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 3 , May 1987 , pp. 405 - 420
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bourbaki, N.. Groupes et algèbres de Lie, chapitres 4–6. Actualités Sci. Indust. 1337 (Hermann, 1968).Google Scholar
[2]Carter, R. W.. Simple groups of Lie type (J. Wiley, 1972).Google Scholar
[3]Carter, R. W.. Conjugacy classes in Weyl groups. Composito Math. 25 (1972), 1–59.Google Scholar
[4]Carter, R. W.. Centralizers of semisimple elements in finite groups of Lie type. Proc. London Math. Soc. (3) 37 (1978), 491–507.CrossRefGoogle Scholar
[5]Deriziotis, D. I.. The centralizers of semisimple elements of the Chevalley groups E 7 and E 8. Tokyo J. of Math. 6 (1983), 191–216.CrossRefGoogle Scholar
[6]Deriziotis, D. I. and Liebeck, M.. Centralizers of semisimple elements in finite twisted groups of Lie type. J. London Math. Soc. (2) 31 (1985), 48–54.CrossRefGoogle Scholar
[7]Dynkin, E. B.. Semisimple subalgebras of semisimple Lie algebras. Amer. Math. Soc. Transl. (2) 6 (1957), 111–244.Google Scholar
[8]Howlett, R. B.. Normalizers of parabolic subgroups of reflection groups. J. London Math. Soc. (2) 21 (1980), 62–80.Google Scholar
[9]Howlett, R. B. and Kilmoyer, R. W.. Principal series representations of finite groups with split BN-pairs. Comm. Algebra 8 (1980), 543–583.Google Scholar
[10]Humphreys, J. E.. Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics 9 (Springer-Verlag, 1972).CrossRefGoogle Scholar
[11]Idowu, A. J.. Combinatorial aspects of the representation theory of Weyl groups. Ph.D. thesis, University of Wales, 1984.Google Scholar
[12]Morris, A. O.. Representations of Weyl groups over an arbitrary field. Astérisque 87–88 (1981), 267–287.Google Scholar