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

We investigate the structure of the ring ${\mathbb D}_G(X)$ of $G$-invariantdifferential operators on a reductive spherical homogeneous space $X=G/H$ withan overgroup $\widetilde{G}$. We consider three natural subalgebras of${\mathbb D}_G(X)$ which are polynomial algebras with explicit generators,namely the subalgebra ${\mathbb D}_{\widetilde{G}}(X)$ of$\widetilde{G}$-invariant differential operators on $X$ and two othersubalgebras coming from the centers of the enveloping algebras of $\mathfrak g$and $\mathfrak k$, where $K$ is a maximal proper subgroup of $G$ containing$H$. We show that in most cases ${\mathbb D}_G(X)$ is generated by any two ofthese three subalgebras, and analyze when this may fail. Moreover, we findexplicit relations among the generators for each possible triple$(\widetilde{G},G,H)$, and describe "transfer maps" connecting eigenvalues for${\mathbb D}_{\widetilde{G}}(X)$ and for the center $Z({\mathfrak g}_{\mathbbC})$ of the enveloping algebra of ${\mathbb g}_{\mathbb C}$.

Invariant differential operators on spherical homogeneous spaces with overgroups