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
    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

    Identifiers