Suppose $G$ is semisimple Lie group, $\mathfrak{g}$ is its Lie algebra, $\mathfrak{h}$ is a Cartan subalgebra of $\mathfrak{g}$, and $W$ is the correspondent Weyl group.


Chevalley restriction theorem says that there is isomorphism of algebras of invariants $\mathbb{C}[\mathfrak{g}]^{G}\simeq \mathbb{C}[\mathfrak{h}]^{W}$ given by restriction.
Here $\mathbb{C}[\mathfrak{g}]$ and $\mathbb{C}[\mathfrak{h}]$ denote the algebras of polynomial functions on correspondent algebras viewed as vector spaces. In other words, $\mathbb{C}[\mathfrak{g}]=Sym(\mathfrak{g}^\*)$ is a symmetric algebra.


My question is: is there a similar result for algebra of $G$-invariants of the exterior algebra $\bigwedge(\mathfrak{g}^\*)$? 


Thank you very much!



Chevalley restriction theorem for exterior algebras
See: [arXiv:dg-ga/9406006](http://arxiv.org/abs/dg-ga/9406006) and [arXiv:math.DG/9506223](http://arxiv.org/abs/math/9506223).


* Edit:


See lemma 3.3 in the first paper: $C^\infty$ and polynomial (by Solomon, cited in the paper)
$W$-invariant differential forms on $\mathfrak h$ correspond to horizontal $G$-invariant forms on $\mathfrak g$. 


I just noted: You are asking for $G$-invariants of $\bigwedge \mathfrak g^\star$, i.e., constant differential forms.  

These describe the de Rham cohomology of a compact form of $G$, by the theorem of Chevalley and Eilenberg, and can be described as the set of primitive elements. See books, for example, 


* MR0400275 (53 #4110) Reviewed 
Greub, Werner; Halperin, Stephen; Vanstone, Ray
Connections, curvature, and cohomology. 
Volume III: Cohomology of principal bundles and homogeneous spaces. Pure and Applied Mathematics, Vol. 47-III. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. xxi+593 pp.
* MR1379333 (97j:57057) Reviewed 
Onishchik, A. L.(RS-YAR)
\cyr Topologiya tranzitivnykh grupp preobrazovaniĭ. (Russian. English, Russian summary) [Topology of transitive transformation groups] Fizmatlit ``Nauka'', Moscow, 1995. 384 pp. ISBN: 5-02-014724-9


There is a translation into English which cannot be found in MathRev:


* Onishchik, Arkadi L.
Topology of transitive transformation groups. (English) Zbl 0796.57001
Leipzig: Johann Ambrosius Barth. xv, 300 p. (1994).


