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Ryo Fujita: Deformed Cartan matrices and generalized preprojective algebras
mercredi 27 octobre 2021, 16:15 - 17:15
Résumé
In their study of deformed W-algebras associated with complex simple Lie algebras, E. Frenkel-Reshetikhin (1998) introduced certain two parameter deformations of the Cartan matrices. They play an important role in the representation theory of quantum affine algebras. In this talk, we explain a representation-theoretic interpretation of these deformed Cartan matrices and their inverses in terms of the generalized preprojective algebras recently introduced by Geiss-Leclerc-Schröer (2017). We also discuss its application to the representation theory of quantum affine algebras in connection with the theory of cluster algebras. This talk is based on a joint work with Kota Murakami (arXiv:2109.07985).