Integral invariant functions on the nilpotent elements of a semisimple Lie algebra
Michael A. Gauger
Proc. Amer. Math. Soc. 68 (1978), 161-164
Primary 17B20; Secondary 22E60
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Abstract: Let L be a semisimple Lie algebra over an algebraically closed field of characteristic zero. It is shown that there is a finitely generated ring R of integral invariant functions such that for nilpotent elements x and y of L, one has x conjugate to y if and only if for all f in R. The result is analogous to Chevalley's determination of conjugacy classes of semisimple elements by the ring of invariant polynomial functions.
A. Gauger, Conjugacy in a semisimple Lie algebra is determined by
similarity under fundamental representations, J. Algebra
48 (1977), no. 2, 382–389. MR 0453827
Kostant, Lie group representations on polynomial rings, Amer.
J. Math. 85 (1963), 327–404. MR 0158024
C. C. MacDuffe, The theory of matrices, Chelsea, New York, 1946.
- M. Gauger, Conjugacy in a semi-simple Lie algebra is determined by similarity under fundamental representations, J. Algebra (to appear). MR 0453827 (56:12080)
- B. Kostant, Lie group representations on polynomial rings, Amer. J. Math. 85 (1963), 327-404. MR 0158024 (28:1252)
- C. C. MacDuffe, The theory of matrices, Chelsea, New York, 1946.
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