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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Given a quasi-split reductive group $G$ and a symmetric variety $X$, weintroduce a notion of endoscopic varieties for $(G,X)$, and establish thefoundational properties of these varieties such as matching of stablesemi-simple orbits. To do this, we introduce certain automorphism groups ofhomogeneous spherical varieties, which encode the fine rational structureneeded to work over non-algebraically closed fields. In particular, weestablish the existence and uniqueness of the corresponding symmetric varietiesunder a mild restriction of the characteristic of the field of definition. Weconjecture that this construction plays a role analogous to endoscopic groupsin the context of the relative trace formula. As evidence, we show how ourconstruction gives a pre-stabilization of regular elliptic terms of relativetrace formulae for many pairs $(G,X)$.  When the cotangent bundle of the symmetric variety is hyperspherical, werelate our theory to the Hamiltonian variety of the Langlands dual groupintroduced by Ben-Zvi, Sakellaridis, and Venkatesh, proving some structuralconjectures for this variety in the symmetric setting.

Symmetric varieties for endoscopic groups