论文信息 - ON CLASSICAL INVARIANT THEORY

ON CLASSICAL INVARIANT THEORY

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.

R. Howe | Roger Howe

[1] H. Weyl. The Classical Groups , 1939 .

[2] R. Thrall,et al. On Symmetrized Kronecker Powers and the Structure of the Free Lie Ring , 1942 .

[3] S. Chern. On a Generalization of Kähler Geometry , 1957 .

[4] A. Weil. Introduction a L'Etude des Varietes Kahleriennes , 1960 .

[5] V. Kac. SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH , 1968 .

[6] P. M. Cohn. ALGEBRES DE LIE SEMI‐SIMPLES COMPLEXES , 1968 .

[7] Sigurdur Helgason,et al. A duality for symmetric spaces with applications to group representations , 1970 .

[8] Masahiko Saito. Représentations unitaires des groupes symplectiques , 1972 .

[9] D. P. Zhelobenko. Compact Lie Groups and Their Representations , 1973 .

[10] S. Gelbart. Holomorphic discrete series for the real symplectic group , 1973 .

[11] Ray A. Kunze,et al. Bessel functions and representation theory. I , 1976 .

[12] B. Kostant,et al. Graded manifolds, graded Lie theory, and prequantization , 1977 .

[13] M. Kashiwara,et al. On the Segal-Shale-Weil representations and harmonic polynomials , 1978 .

[14] 公庄庸三. Basic Algebra = 代数学入門 , 2002 .

[15] D. Littlewood,et al. The Theory of Group Characters and Matrix Representations of Groups , 2006 .