Tannakian classification of equivariant principal bundles on toric varieties
Indranil Biswas, Arijit Dey, Mainak Poddar

TL;DR
This paper extends Klyachko's classification of equivariant vector bundles on toric varieties to principal G-bundles using Tannakian formalism, establishing an equivalence of categories in characteristic zero.
Contribution
It introduces compatible Σ-filtered algebras to classify equivariant principal G-bundles on toric varieties, generalizing previous vector bundle classifications.
Findings
Establishes an equivalence between T-equivariant principal G-bundles and compatible Σ-filtered algebras.
Generalizes Klyachko's vector bundle classification to principal G-bundles.
Applicable in characteristic zero fields.
Abstract
Let be a complete toric variety equipped with the action of a torus and a reductive algebraic group, defined over an algebraically closed field . We introduce the notion of a compatible --filtered algebra associated to , generalizing the notion of a compatible --filtered vector space due to Klyachko, where denotes the fan of . We combine Klyachko's classification of --equivariant vector bundles on with Nori's Tannakian approach to principal --bundles, to give an equivalence of categories between --equivariant principal --bundles on and certain compatible --filtered algebras associated to , when the characteristic of is .
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