Abstract
Let L be a group, V a finite dimensional complex vector space and φ : L → GL(V) a representation. Let us denote by S’(V) the ring of all polynomial functions on V; clearly L acts on S’(V). The main problem of the classical invariant theory can be phrased as follows: To find explicitly all the L-invariant polynomial functions on V.
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References
Andruskiewitsch, N., On the complicatedness of the pair (g,K), Rev. Mat. Univ. Complut. Madrid 2 1 (1989), 12–28.
A new proof of Tirao’s Restriction Theorem,Revista de la UMA (To appear).
Computing some rings of invariants,Proceedings of the IX ELAM (To appear).
Andruskiewitsch, N., Tirao, J., A Restriction Theorem for modules having a spherical submodule,Trans. AMS (To appear).
Brega, O.A. and Tirao, J. A., A property of a distinguished class of K-modules associated to the classical rank one semisimple Lie algebras,Proc. oof the IX ELAM ( To appear).
Brion, M., Luna, D. and Vust, Th, Espaces homogenes spheriques, Inv. Math. 84 (1986), 617–632.
Elashvili, A.G., Canonical form and stationary subalgebras of points of general position for simple linear Lie groups,Funct. Anal. Appl. 6(1972).
Kac, V.G., Some remarks on nilpotent orbits,Journal of Algebra 64 (1980),190–213
Kostant, B., Lie group representations on polynomial rings, Amer. J. of Math. 85 (1963), 327–404.
Kostant, B. and Rallis, S., Orbits and representations associated with symmetric spaces, Amer. J. of Math. 93 (1971), 753–809.
Kostant, B. and Tirao, J.A., On the structure of certain subalgebras of a universal enveloping algebra, Trans. AMS 218 (1976), 133–154.
Luna, D. and Richardson R.W., A generalization of the Chevalley Restriction Theorem, Duke J. of Math. 46 (1979), 487–497.
Mumford, D., “Geometric Invariant Theory,” Springer-Verlag, 1980. 2nd. edition.
Tirao, J., A Restriction Theorem for Semisimple Lie Groups of Rank One, Trans. A.M.S. 279 (1983), 651–660.
Vinberg, E.B. and Kimel’feld,B.N., Homogeneous domains on flag manifolds and spherical subgroups, Funct. Anal. Appl. 12 (1978), 168–174.
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© 1992 Birkhäuser Boston
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Andruskiewitsch, N. (1992). On Spherical Modules. In: Tirao, J., Wallach, N.R. (eds) New Developments in Lie Theory and Their Applications. Progress in Mathematics, vol 105. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2978-0_12
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DOI: https://doi.org/10.1007/978-1-4612-2978-0_12
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