Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-06T02:02:23.534Z Has data issue: false hasContentIssue false
  • English
  • Français

Hall–Littlewood polynomials at roots of 1 and modular representations of the symmetric group

Published online by Cambridge University Press:  24 October 2008

A. O. Morris  and
N. Sultana
A. O. Morris
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth, Dyfed SY23 3BZ
N. Sultana
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth, Dyfed SY23 3BZ
Get access Rights & Permissions [Opens in a new window]

Extract

We first give a brief introduction to Hall–Littlewood functions; we follow closely the notation used in Macdonald [3].

Let λ = (λ1,…,λm) be a be a partition of n; that is λ1 + … + λm = n, λ1 ≥ λ2 ≥ … ≥ λm >0. We shall sometimes write l(λ) for m and refer to l(λ) as the length of λ and we shall write |λ| for ∑λi. Let x1, x2, … be an infinite set of indeterminates and t an indeterminate independent of the xi (i = 1,2, …). Let Pλ(x;t) = Pλ(x1, x2, …t) and Qλ(x,t) = Qλ(xl, x2, …t) be the Hall–Littlewood P- and Q-functions defined as in Macdonald.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 443 - 453
Copyright
Copyright © Cambridge Philosophical Society 1991

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]James, G. D.. The decomposition matrices of GLn(q) for n ≥ 10. Proc. London Math Soc. (3) 60 (1990), 225–265.Google Scholar
[2]James, G. D. & Kerber, A.. The Representation Theory of the Symmetric Group (Addison Wesley, 1981).Google Scholar
[3]Macdonald, I. G.. Symmetric Functions and Hall Polynomials (Clarendon Press, 1979).Google Scholar
[4]Morris, A. O.. On an algebra of symmetric functions. Quart. J. Math. Oxford Ser. (2) 16 (1965), 5–64.CrossRefGoogle Scholar
[5]Robinson, G. de B.. Representation Theory of the Symmetric Group (Edinburgh University Press, 1961).Google Scholar
[6]Sultana, N.. Hall–Littlewood polynomials and their applications to representation theory. Ph.D. thesis, University of Wales (1990).Google Scholar