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Partial flag varieties and preprojective algebras

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arxiv math/0609138 v3 pith:JWU2MDVE submitted 2006-09-05 math.RT math.AG

Christof Geiss , Bernard Leclerc , Jan Schröer This is my paper · ORCID
classification math.RTmath.AG
keywords algebraflagmodulespartialpreprojectiverigidvarietiesalgebraic
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Let L be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected algebraic group. We study rigid modules in subcategories sub(Q) for Q an injective L-module, and we introduce a mutation operation between complete rigid modules in sub(Q). This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G.

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  1. Singularities of massless scattering and cluster algebras

    hep-th 2025-07 conditional novelty 5.0 of 10

    Partial flag cluster algebras reproduce a large part of the two-loop five- and six-point massless scattering symbol alphabets, with the momentum twistor embedding stronger at six points after permutation completion.

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