Classification of \(A_{\mathfrak{q}}(\lambda)\) modules by their Dirac cohomology for type \(D\), \(G_{2}\) and \(\mathfrak{sp}(2 n, \mathbb{R})\) (Q1734229)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification of \(A_{\mathfrak{q}}(\lambda)\) modules by their Dirac cohomology for type \(D\), \(G_{2}\) and \(\mathfrak{sp}(2 n, \mathbb{R})\) |
scientific article |
Statements
Classification of \(A_{\mathfrak{q}}(\lambda)\) modules by their Dirac cohomology for type \(D\), \(G_{2}\) and \(\mathfrak{sp}(2 n, \mathbb{R})\) (English)
0 references
22 March 2019
0 references
Let $G$ be a connected real reductive group and $\Theta$ a Cartan involution on $G$ such that $K=G^{\Theta}$ is a maximal compact subgroup of $G$. The paper under review describes admissible $\Theta$-stable parabolic subalgebras of the corresponding Lie algebra $\mathfrak{g}$ in types $D$ and $G_2$ and in the case $\mathfrak{g}_0=\mathfrak{sp}(2n,\mathbb{R})$.
0 references
Dirac cohomology
0 references
reductive group
0 references
maximal compact subgroup
0 references
Cartan involution
0 references
infinitezimal character
0 references
0 references