Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T08:56:28.457Z Has data issue: false hasContentIssue false
  • English
  • Français

A Schensted Algorithm Which Models Tensor Representations of the Orthogonal Group

Published online by Cambridge University Press:  20 November 2018

Robert A. Proctor
Robert A. Proctor*
Affiliation:
University of North Carolina, Chapel Hill, North Carolina
Rights & Permissions [Opens in a new window]

Extract

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.

This paper is concerned with a combinatorial construction which mysteriously “mimics” or “models” the decomposition of certain reducible representations of orthogonal groups. Although no knowledge of representation theory is needed to understand the body of this paper, a little familiarity is necessary to understand the representation theoretic motivation given in the introduction. Details of the proofs will most easily be understood by people who have had some exposure to Schensted's algorithm or jeu de tacquin.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 1 , 01 February 1990 , pp. 28 - 49
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Berele, A., A Schensted-type correspondence for the symplectic group, J. Combin. Theory A 43 (1986), 320–328.Google Scholar
2. Berele, A. and Regev, A., Hook Young diagrams, combinatorics and representations of Lie superalgebras, Bull. AMS 8 (1983), 337–339.Google Scholar
3. King, R.C. and El-Sharkaway, N.G.I., Standard Young tableaux and weight multiplicities of the classical Lie groups, J. Physics A 16 (1983), 3153–3178.Google Scholar
4. Koike, K. and Terada, I., Young-diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank, Advances in Math., to appear.Google Scholar
5. Hanlon, P. and Wales, D., On the decomposition of Brauer s centralizer algebras, J. Algebra, to appear.Google Scholar
6. Proctor, R., Young tableaux, Gelfand patterns, and branching rules for classical Lie groups, preprint.Google Scholar
7. Proctor, R., A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups, Trans. AMS, to appear.Google Scholar
8. Proctor, R., Interconnections between symplectic and orthogonal characters, in Proceedings of a special session on invariant theory, Contemporary Mathematics (Amer. Math. Soc, Providence, 1989).Google Scholar
9. Schensted, C., Longest increasing and decreasing subsequences, Can. J. Math. 13 (1961), 179— 191.Google Scholar
10. Stembridge, J., Rational tableaux and the tensor algebra of gln, J. Combin. Theory A 46 (1987), 79–120.Google Scholar
11. Sundaram, S., Orthogonal tableaux and an insertion algorithm for SO(2n+l), J. Combin. Theory A, to appear.Google Scholar
12. Sundaram, S., On the combinatorics of representations of Sp(2n,C), doctoral thesis, M.I.T. (1986).Google Scholar
13. Sundaram, S., The Cauchy identity for Sp(2n), J. Combin. Theory A, to appear.Google Scholar
14. Weyl, H., The classical groups, 2nd ed (Princeton University Press, Princeton, 1946).Google Scholar