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}
}
  • F. Knop
  • Published 1 September 1994
  • Mathematics
  • Annals of Mathematics
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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