References
[AbMa] Abraham, R., Marsden, J.: Foundations of Mechanics, 2nd ed. Reading, Mass.: Benjamin/Cummings 1978
[Baur] Bauer, F.L.: Zur Theorie der Spingruppen. Math. Ann.128, 229–256 (1954)
[Brbk] Bourbaki, N.: Groupes et algèbres de Lie. Chapitres 4, 5 et 6. Paris: Hermann 1968
[Cart] Cartan, E.: Les groupes de transformations continus, infinis, simples. Ann. Sci. Ec. Norm. Super., IV. Ser26, 93–161 (1909) in Pt. II, Vol. 2, Oeuvers Complètes.
[GeZv] Gelfand, I.M., Zelevinsky, A.V.: Models of representations of classical groups and their hidden symmetries. Funct. Anal. Appl.18, 183–198 (1984)
[GeZt] Gelfand, I.M., Zetlin, M.L.: Finite-dimensional representations of the orthogonal group. Math. USSR Doklady71, 1070–1080 (1950) (Russian)
[GsVi] Gessel, I., Viennot, G.: Determinants, paths, and plane partitions, in preparation
[Herm] Hermann, R.: Sophus Lie's 1884 differential invariant paper. Brookline, Ma.: Math Sci. Press 1975
[Hmph] Humphreys, J.: Introduction to Lie algebras and representation theory. Berlin-Heidelberg-New York: Springer 1979
[Jacb] Jacobson, N.: Lie algebras. New York: J. Wiley and Sons 1962
[Kng1] King, R.C.: Weight multiplicities for classical groups. In: Janner, A., Janssen, T., Boon, M. (eds.), Group theoretical methods in physics (Lect. Notes Phys., vol. 50. Berlin-Heidelberg-New York: Springer 1976
[Kng2] El Samra, N., King, R.C.: Dimensions of irreducible representations of the classical groups. J. Phys. A12, 2317–2328 (1979)
[Kng3] King, R.C., El-Sharkaway, N.G.I.: Standard Young tableaux and weight multiplicities of the classical Lie groups. J. Phys. A16, 3153–3178 (1983)
[Kng4] El Samra, N., King, R.C.: Reduced determinantal forms for characters of the classical Lie groups. J. Phys. A12, 2035–2315 (1979)
[KoT1] Koike, K., Terada, I.: Young-diagrammatic methods for the representation theory of the classical groups of type B n , C n , D n . J. Algebra107 466–511 (1987)
[KoT2] Koike, K., Terada, I.: Young-diagrammatic methods for the restriction of complex classical Lie groups to reductive subgroups of maximal rank. Adv. Math. (to appear)
[Lie] Lie, S.: Über Differentialinvarianten. Math. Ann.24, 537–578 (1884)
[Litt] Littlewood, D.E.: The theory of group characters, 2nd Edition. Oxford University Press, London, 1950
[MacM] MacMahon, P.A.: Combinatory analysis Vol. 2. Cambridge: The University Press, 1916
[Mcd1] Macdonald, I.G.: Affine root systems and Dedekind's η-function. Invent. Math.15, 91–143 (1972)
[Mcd2] Macdonald, I.G.: Symmetric functions and Hall polynomials. Oxford University Press, London, 1979
[Prc1] Proctor, R.: A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups. Preprint
[Prc2] Proctor, R.: Interconnections between symplectic and orthogonal characters. In: Lakshmibai, V. (ed.) Proceedings of a special session on invariant theory. Contemporary Mathematics, Am. Math. Soc. (to appear)
[Prc3] Proctor, R.: Classical Gelfand-Young patterns, unpublished research announcement, May, 1985. (Gelfand patterns and Young tableaux for classical groups; paper in preparation)
[Prc4] Proctor, R.: untitled unpublished research announcement, January 1984. (Some new plane partition identities, paper in preparation.)
[Prc5] Proctor, R.: Odd symplectic groups and combinatorics. In: Britten, D.J., Lemire, F.W., Moody, R.V. (eds.) Lie algebras and related topics. CMS Conf. Proc., vol. 5, Am. Math. Soc., Providence, 1986
[SiSt] Singer, I.M., Sternberg, S.: On the infinite groups of Lie and Cartan. J. Anal. Math.15, 1–114 (1965)
[Stn1] Stanley, R.: Some combinatorial aspects of the Schubert calculus. In: Foata, D. (ed.) Combinatoire et représentation du groupe symétrique. Lect. Notes Math., vol. 579. Berlin-Heidelberg-New York: Springer 1977
[Stn2] Stanley, R.: Symmetries of plane partitions. J. Comb. Theory, Ser. A43, 103–113 (1986)
[Weyl] Weyl, H.: The classical groups, 2nd edition. Princeton University Press, Princeton 1946
[Zhl1] Zhelobenko, D.P.: The classical groups. Spectral analysis of their finite dimensional representations. Russ. Math. Surv.17 1–94 (1962)
[Zhl2] Zhelobenko, D.P.: On Gelfand-Zetlin bases for classical Lie algebras. In: Kirillov, A.A. (ed.) Representations of Lie groups and Lie algebras. Budapest: Akademiai Kiado 1985
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Supported in part by a Bantrell Foundation Fellowship and an NSF Mathematical Sciences Postdoctoral Fellowship
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Proctor, R.A. Odd symplectic groups. Invent Math 92, 307–332 (1988). https://doi.org/10.1007/BF01404455
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DOI: https://doi.org/10.1007/BF01404455