Dipartimento di Scienze di Base e Applicate per l'Ingegneria

We aim at studying the connection between Nakajima quiver varieties, quantum affine algebras and cluster algebras. After the

work of many authors (Keller, Scherodtzke, Hernandez, Leclerc, Plamondon, Cerulli Irelli, Reineke, Feigin...) it is known that

some (graded) Nakajima quiver varieties can be realized as variety of representations of some finite dimensional algebras.

Moreover it is known that the closure of the orbits of representations of these algebras can be realized as a geometric quotient

of such Nakjaima quiver varieties. We aim at studying the theory of Nakajima quiver varieties in order to deduce information

about geometric properties of the orbit closures in the case of Dynkin quivers. The construction of the isomorphism passes by

the knowledge of representation theory of quantum affine algebras.

 

Participants: 

 

Giovanni Cerulli Irelli

Elena Pascucci

Francesca Paganelli

Javier De Loera Chavez