Partial flag varieties and preprojective algebras
Annales de l'Institut Fourier, Volume 58 (2008) no. 3, p. 825-876

Let Λ be a preprojective algebra of type A,D,E, and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ-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.

Soit Λ une algèbre préprojective de type A,D,E, et soit G le groupe algébrique complexe semi-simple et simplement connexe correspondant. Nous étudions les modules rigides des sous-catégories Sub QQ désigne un Λ-module injectif, et nous introduisons une opération de mutation sur les modules rigides complets de Sub Q. Ceci conduit à des structures d’algèbre amassée sur les anneaux de coordonnées des variétés de drapeaux partiels associées à G.

DOI : https://doi.org/10.5802/aif.2371
Classification:  14M15,  16D90,  16G20,  16G70,  17B10,  20G05,  20G20,  20G42
Keywords: Flag variety, preprojective algebra, Frobenius category, rigid module, mutation, cluster algebra, semicanonical basis
@article{AIF_2008__58_3_825_0,
     author = {Gei\ss , Christof and Leclerc, Bernard and Schr\"oer, Jan},
     title = {Partial flag varieties and preprojective algebras},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {3},
     year = {2008},
     pages = {825-876},
     doi = {10.5802/aif.2371},
     mrnumber = {2427512},
     zbl = {1151.16009},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2008__58_3_825_0}
}
Geiß, Christof; Leclerc, Bernard; Schröer, Jan. Partial flag varieties and preprojective algebras. Annales de l'Institut Fourier, Volume 58 (2008) no. 3, pp. 825-876. doi : 10.5802/aif.2371. http://www.numdam.org/item/AIF_2008__58_3_825_0/

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