Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-07-01T20:18:42.355Z Has data issue: false hasContentIssue false
  • English
  • Français

On the characters of the Weyl group of type D

Published online by Cambridge University Press:  24 October 2008

S. J. Mayer
S. J. Mayer
Affiliation:
Queen Mary College, London
Get access Rights & Permissions [Opens in a new window]

Extract

This paper is a continuation of (2), (3) in the development of a unified theory of the characters of the Weyl groups of the simple Lie algebras using their common structure as reflection groups; compare Carter (1) for a similar development for the conjugacy classes. We look at the Weyl group of type D, which is a subgroup of index two in the Weyl group of type C. It was first studied by Young (4), but rather less is known about the characters of this group than those of types A and C. Indeed, the situation is rather more complicated, but we are able to give, as before, an algorithm to determine irreducible constituents of the principal character of a Weyl subgroup induced up to the whole group. We shall also study the case where the rank of the Weyl group is even, when extra irreducible characters may arise, and after constructing these, we shall state some results on their occurrence in the induced principal character.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 2 , March 1975 , pp. 259 - 264
Copyright
Copyright © Cambridge Philosophical Society 1975

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)Carter, R. W.Conjugacy classes in the Weyl group, Seminar on algebraic groups and related finite groups (Springer lecture notes in mathematics, vol. 131, 1970).Google Scholar
(2)Mayer, S. J.On the irreducible characters of the symmetric group. Advances in Mathematics. 14 (1974).Google Scholar
(3)Mayer, S. J.On the characters of the Weyl group of type C. J. Algebra 33 (1975).CrossRefGoogle Scholar
(4)Young, A.On quantitative substitutional analysis: V. Proc. London Math. Soc. (2), 31 (1930), 273–288.CrossRefGoogle Scholar