Partial flag varieties and preprojective algebras

Details Partial flag varieties and preprojective algebras Partial flag varieties and preprojective algebras

2006-09-05

arxiv.org/abs/math/0609138v3

Mathematics

Representation Theory

42 pages, 12 figures, 4 tables. Version 3 : minor corrections and one reference added. Final version to appear in Annales de l

Scientific paper

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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