Higher-dimensional representations of \(\mathsf {SL}_2\) and its real forms via Plücker embedding (Q1695151)

The paper under review studies representations of the complex Lie group \(SO_3\) and its real forms which arise from the inclusion map \(\mathfrak{sl}_2\cong \mathfrak{so}_3\subset \mathfrak{so}_n\) realized via the Plücker embedding. Explicit matrix realizations together with Euler and Wigner decompositions are constructed in this setting and examples of \(n=3,4,5\) are given in detail. The paper is written in a fairly informal way without explicit emphasized statements.