A generating function of strict Gelfand patterns and some formulas on characters of general linear groups

Takeshi TOKUYAMA

doi:10.2969/jmsj/04040671

Takeshi TOKUYAMA

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ジャーナルフリー

1988 年 40 巻 4 号 p. 671-685

DOI https://doi.org/10.2969/jmsj/04040671

詳細

Published: 1988 Received: 1987/05/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) L. C. Biedenharn and J. D. Louck, The Racah-Wigner Algebra in Quantum Theory, Encyclopedia Math. Appl., 9, Addison-Wesley, Mass., 1981.
2) N. Bourbaki, Groupes et algebre de Lie, chap. 4, 5, 6, Hemann, Paris, 1968.
3) N. Bourbaki, Groupes et algebre de Lie, chap. 9, Masson, Paris, 1982.
4) I. M. Gelfand and M. L. Zetlin, Matrix elements for the unitary groups, Dokl. Akad. Nauk SSSR, 71 (1950), 825-828.
5) H. Hiller, Geometry of Coxeter Groups, Pitman, London, 1982.
6) V. G. Kac, Infinite dimensional Lie algebras, 2nd ed., Cambridge Univ. Press, 1985.
7) D. E. Littlewood, The Theory of Group Characters, 2nd ed., Oxford Univ. Press, 1950.
8) I. G. MacDonald, Symmetric Functions and Hall Polynomials, Oxford Math. Monographs, Oxford Univ. Press, 1979.
9) W. H. Mills, D. P. Robbins and H. R. Rumsey Jr., Alternating sign matrices and descending plane partitions, J. of Combinatorial Theories (A), 34 (1983), 340-359.
10) R. P. Stanley, A Bakers dozen of conjectures concerning plane partitions, in Combinatoire enumerative, Lecture Note in Math., 1234, Springer, 1987, pp. 285-293.
11) T. Tokuyama, Determinantal method and the Littlewood-Richardson rule, to appear in J. of Algebra.
12) H. Weyl, The classical groups, Princeton Math. Series, 1, Princeton Univ. Press, 1939.
13) D. P. Zelovenco, Compact Lie Groups and Their Representations, Trans. Math. Monographs, 42, Amer. Math. Soc., Providence, 1973.
14) Combinatorics and Algebra, (edited by C. Greene), Contemporary Math., 34, Amer. Math. Soc., Providence, 1984.

Right : [1] L. C. Biedenharn and J. D. Louck, The Racah-Wigner Algebra in Quantum Theory, Encyclopedia Math. Appl., 9, Addison-Wesley, Mass., 1981.
[2] N. Bourbaki, Groupes et algebre de Lie, chap. 4, 5, 6, Hemann, Paris, 1968.
[3] N. Bourbaki, Groupes et algebre de Lie, chap. 9, Masson, Paris, 1982.
[4] I. M. Gelfand and M. L. Zetlin, Matrix elements for the unitary groups, Dokl. Akad. Nauk SSSR, 71 (1950), 825-828.
[5] H. Hiller, Geometry of Coxeter Groups, Pitman, London, 1982.
[6] V. G. Kac, Infinite dimensional Lie algebras, 2nd ed., Cambridge Univ. Press, 1985.
[7] D. E. Littlewood, The Theory of Group Characters, 2nd ed., Oxford Univ. Press, 1950.
[8] I. G. MacDonald, Symmetric Functions and Hall Polynomials, Oxford Math. Monographs, Oxford Univ. Press, 1979.
[9] W. H. Mills, D. P. Robbins and H. R. Rumsey Jr., Alternating sign matrices and descending plane partitions, J. of Combinatorial Theories (A), 34 (1983), 340-359.
[10] R. P. Stanley, A Bakers dozen of conjectures concerning plane partitions, in Combinatoire enumerative, Lecture Note in Math., 1234, Springer, 1987, pp. 285-293.
[11] T. Tokuyama, Determinantal method and the Littlewood-Richardson rule, to appear in J. of Algebra.
[12] H. Weyl, The classical groups, Princeton Math. Series, 1, Princeton Univ. Press, 1939.
[13] D. P. Zelovenco, Compact Lie Groups and Their Representations, Trans. Math. Monographs, 42, Amer. Math. Soc., Providence, 1973.
[14] Combinatorics and Algebra, (edited by C. Greene), Contemporary Math., 34, Amer. Math. Soc., Providence, 1984.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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