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Universal induced characters and restriction rules for the classical groups

Published online by Cambridge University Press:  22 January 2016

Yasuo Teranishi
Yasuo Teranishi*
Affiliation:
Universität Mannheim, Lehrstuhl für Mathematik VI, 6800 Mannheim 1, Federal Republic of Germany and Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan
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The purpose of this paper is the study of some basic properties of universal induced characters and their applications to the representation theory of the classical groups (for the definition of a universal induced character, see § 3).

The starting point was the paper [F] by E. Formanek on matrix invariants. In his paper [F], Formanek has investigated the Hilbert series for the ring of matrix invariants from the point of view of the representation theory of the general linear group and the symmetric group. In this paper we shall study polynomial concomitants of a group from the same point of view.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 117 , March 1990 , pp. 173 - 205
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[F] Formanek, E., Invariants and the ring of generic matrices, J. Algebra, 89 (1984), 178–223.CrossRefGoogle Scholar
[G] Green, J. A., “Polynomial Representations of GLn ,” Lecture Notes in Mathematics No. 830, Springer Verlag, Berlin/Heidelberg/New York, 1980.Google Scholar
[H-R] Hochster, M. and Roberts, J. L., Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. in Math., 13 (1974), 115–175.CrossRefGoogle Scholar
[K-1] King, R. C., Modification rules and products of irreducible representations of unitary, orthogonal, and symplectic groups, J. Math. Phys., 12 (1971), 1588–1598.CrossRefGoogle Scholar
[K-2] King, R. C., Branching rules for classical Lie groups using tensor and spinor methods, J. Phys., A 8 (1975), 429–449.Google Scholar
[K-T] Koike, K. and Terada, I., Young diagrammatic methods for representation theory of the classical groups of type B n , C n , D n , J. Algebra, 107 (1987), 466–511.CrossRefGoogle Scholar
[L] Littlewood, D. E., “The Theory of Group Characters and Matrix Representations of Groups,” Oxford Univ. Press, London, 1950.Google Scholar
[M] Macdonald, I. G., “Symmetric Functions and Hall Polynomials,” Oxford Univ. Press, Oxford, 1979.Google Scholar
[P] Procesi, C., The invariant theory of n × n matrices, Adv. in Math., 19 (1976), 306–381.Google Scholar
[R] Razmyslov, Y. P., Trace identities of full matrix algebras over a field of characteristic zero, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 723–756 (Russian); Math. USSR Izv. 8 (1974), 727–760 (English Translation).Google Scholar
[S] Schur, I., Über eine Klasse von Matrizen die sich einer gegebenen Matrix zuordonen lassen, Dissertation 1901, Berlin. (= Ges. Abhandlungen Bd I, 1–72).Google Scholar
[S] Stanley, R., Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc., 1 (1979), 475–511.CrossRefGoogle Scholar
[T] Teranishi, Y., The Hilbert series of rings of matrix concomitants, Nagoya Math. J., 111 (1988), 143–156.CrossRefGoogle Scholar
[W-1] Weyl, H., Zur Darstellungstheorie und Invariantenabzälung der projectiven, der Komplex- und der Drehungsgruppe, Ges. Abhandlungen Bd III, p. 1–25, Springer-Verlag, Berlin/Heidelberg/New York, 1968.Google Scholar
[W-2] Weyl, H., “The Classical Groups,” Princeton Univ. Press, Princeton, N.J., 1946.Google Scholar