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

A toric principal $G$-bundle is a principal $G$-bundle over a toric varietytogether with a torus action commuting with the $G$-action. In a recent paper,extending the Klyachko classification of toric vector bundles, Chris Manon andthe second author give a classification of toric principal bundles using"piecewise linear maps" to the (extended) Tits building of $G$. In this paper,we use this classification to give a description of the (equivariant)automorphism group of a toric principal bundle as well as a simple criterionfor (equivariant) reduction of structure group, recovering results of Dasguptaet al. Finally, motivated by the equivariant splitting problem for toricprincipal bundles, we introduce the notion of "Helly's number" of a buildingand pose the problem of giving sharp upper bounds for Helly's number of Titsbuildings of semisimple algebraic groups $G$.

Toric principal bundles, Tits buildings and reduction of structure group