# A Harish-Chandra homomorphism for reductive group actions

@article{Knop1994AHH, title={A Harish-Chandra homomorphism for reductive group actions}, author={Friedrich Knop}, journal={Annals of Mathematics}, year={1994}, volume={140}, pages={253-288} }

Consider a semisimple complex Lie algebra g and its universal enveloping algebra U(g). In order to study unitary representations of semisimple Lie groups, Harish-Chandra ([HC1] Part III) established an isomorphism between the center Z(g) of U(g) and the algebra of invariant polynomials C[t] . Here, t ⊆ g is a Cartan subspace and W is the Weyl group of g. This is one of the most basic results in representation theory. Later on ([HC2] Thm. 1), he found a similar isomorphism for a symmetric space…

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