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Chevalley restriction theorem
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In the mathematical theory of Lie groups, the Chevalley restriction theorem describes functions on a Lie algebra which are invariant under the action of a Lie group in terms of functions on a Cartan subalgebra.
Statement
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Perspective
Chevalley's theorem requires the following notation:
Chevalley's theorem asserts that the restriction of polynomial functions induces an isomorphism
- .
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Proofs
Humphreys (1980) gives a proof using properties of representations of highest weight. Chriss & Ginzburg (2010) give a proof of Chevalley's theorem exploiting the geometric properties of the map .
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References
- Chriss, Neil; Ginzburg, Victor (2010). Representation theory and complex geometry. Birkhäuser. doi:10.1007/978-0-8176-4938-8. ISBN 978-0-8176-4937-1. S2CID 14890248. Zbl 1185.22001.
- Humphreys, James E. (1980). Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics. Vol. 9. Springer. Zbl 0447.17002.
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