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Partial flag varieties and preprojective algebras

Christof Geiss·Bernard Leclerc·Jan Schröer
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Abstract

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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Christof Geiss, Bernard Leclerc, Jan Schröer. 2006-09-05. Partial flag varieties and preprojective algebras. https://arxiv.org/abs/math/0609138

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