English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{p}$ be the Cartandecomposition of the complexified Lie algebra$\mathfrak{g}=\mathfrak{sl}(3,\mathbb{C})$ of the group $G=SU(2,1)$. Let$K=S(U(2) \times U(1))$; so $K$ is a maximal compact subgroup of $G$. Let$U(\mathfrak{g})$ be the universal enveloping algebra of $\mathfrak{g}$, andlet $C(\mathfrak{p})$ be the Clifford algebra with respect to the trace form$B(X,Y)=\text{tr}(XY)$ on $\mathfrak{p}$. We are going to prove that thealgebra of K-invariants in $U(\mathfrak{g}) \otimes C(\mathfrak{p})$ isgenerated by five explicitly given elements. This is useful for studyingalgebraic Dirac induction for $(\mathfrak{g},K)$-modules. Along the way we willalso recover the (well known) structure of the algebra $U(\mathfrak{g})^K$.

K-invariants in the algebra U(g) $\otimes$ C(p) for the group SU(2,1)