Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-16T23:20:33.938Z Has data issue: false hasContentIssue false
  • English
  • Français

THE SYMMETRIC GROUP REPRESENTATION ON COHOMOLOGY OF THE REGULAR ELEMENTS OF A MAXIMAL TORUS OF THE SPECIAL LINEAR GROUP

Part of: General theory of differentiable manifolds Representation theory of groups

Published online by Cambridge University Press:  01 February 2008

ANTHONY HENDERSON
ANTHONY HENDERSON*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia (email: [email protected])
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.

We give a formula for the character of the representation of the symmetric group Sn on each isotypic component of the cohomology of the set of regular elements of a maximal torus of SLn, with respect to the action of the centre.

Keywords

symmetric grouprepresentationcohomology

MSC classification

Secondary: 20C30: Representations of finite symmetric groups 58A10: Differential forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 1 , February 2008 , pp. 85 - 98
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Blair, J. and Lehrer, G. I., ‘Cohomology actions and centralisers in unitary reflection groups’, Proc. London Math. Soc. (3) 83(3) (2001), 582–604.Google Scholar
[2]Dimca, A. and Lehrer, G. I., ‘Purity and equivariant weight polynomials’, in: Algebraic groups and Lie groups, Australian Mathematical Society Lecture Series, 9 (Cambridge University Press, Cambridge, 1997), pp. 161–181.Google Scholar
[3]Fleischmann, P. and Janiszczak, I., ‘The number of regular semisimple elements for Chevalley groups of classical type’, J. Algebra 155 (1993), 482–528.CrossRefGoogle Scholar
[4]Hanlon, P., ‘The characters of the wreath product group acting on the homology groups of the Dowling lattices’, J. Algebra 91 (1984), 430–463.CrossRefGoogle Scholar
[5]Henderson, A., ‘Representations of wreath products on cohomology of De Concini–Procesi compactifications’, Int. Math. Res. Not. 2004(20) (2004), 983–1021.CrossRefGoogle Scholar
[6]Henderson, A., ‘Bases for certain cohomology representations of the symmetric group’, J. Algebraic Combin. 24(4) (2006), 361–390.CrossRefGoogle Scholar
[7]Lehrer, G. I., ‘On hyperoctahedral hyperplane complements’, in: The Arcata Conf. on representations of finite groups (Arcata, CA, 1986), Proceedings of Symposia in Pure Mathematics, 47 (American Mathematical Society, Providence, RI, 1987), pp. 219–234.Google Scholar
[8]Lehrer, G. I., ‘On the Poincaré series associated with Coxeter group actions on complements of hyperplanes’, J. London Math. Soc. (2) 36 (1987), 275–294.Google Scholar
[9]Lehrer, G. I., ‘Poincaré polynomials for unitary reflection groups’, Invent. Math. 120 (1995), 411–425.CrossRefGoogle Scholar
[10]Macdonald, I. G., Symmetric functions and Hall polynomials, 2nd edn (Oxford University Press, Oxford, 1995).Google Scholar