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/

Zendy Plus

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

Zendy Tools

Zendy Open

For local non-archimedean fields $k$ of sufficiently large residualcharacteristic, we explicitly parametrize and count the rational nilpotentadjoint orbits in each algebraic orbit of orthogonal and special orthogonalgroups. We separately give an explicit algorithmic construction forrepresentatives of each orbit. We then, in the general setting of groups$\mathrm{GL}_n(D)$, $\mathrm{SL}_n(D)$ (where $D$ is a central division algebraover $k$) or classical groups, give a new characterisation of the "buildingset" (defined by DeBacker) of an $\mathfrak{sl}_2(k)$-triple in terms of thebuilding of its centralizer. Using this, we prove our construction realizesDeBacker's parametrization of rational nilpotent orbits via elements of theBruhat-Tits building.

Nilpotent orbits of orthogonal groups over $p$-adic fields, and the DeBacker parametrization