Corollary 1

Tag 01J7, permanent. Cite it as [Bourbaki, Tag 01J7].

Lie Groups and Lie Algebras, chapter VIII, § 8. Symmetric invariants

— Let $\mathrm{U}(\mathfrak g)$ be the enveloping algebra of $\mathfrak g$ . Let the homomorphism

\zeta:\mathrm{U}(\mathfrak g)^*\longrightarrow\mathrm{U}(\mathfrak h)^*=\mathrm{S}(\mathfrak h)^*

be the transpose of the canonical injection

\mathrm{U}(\mathfrak h)\longrightarrow\mathrm{U}(\mathfrak g).

The following diagram commutes

\begin{array}{ccccc} \mathscr{R}(\mathfrak g)&\xrightarrow{\mathrm{ch}}&\mathbf{Z}[P]\\ \Big\downarrow{\scriptstyle\mathrm{Tr}}&&\Big\downarrow{\scriptstyle\psi}\\ \mathrm{U}(\mathfrak g)^*&\xrightarrow{\zeta}&\mathrm{S}(\mathfrak h)^* \end{array}

This is simply a reformulation of Prop. 2.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Prop. 2