TY - JOUR

T1 - Homological approach to the hernandez-leclerc construction and quiver varieties

AU - Irelli, Giovanni Cerulli

AU - Feigin, Evgeny

AU - Reineke, Markus

PY - 2014

Y1 - 2014

N2 - In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver varieties. This approach is used to get an explicit realization of the orbit closures of representations of Dynkin quivers as affine quotients.

AB - In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver varieties. This approach is used to get an explicit realization of the orbit closures of representations of Dynkin quivers as affine quotients.

UR - http://www.scopus.com/inward/record.url?scp=84896692853&partnerID=8YFLogxK

U2 - 10.1090/S1088-4165-2014-00449-7

DO - 10.1090/S1088-4165-2014-00449-7

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AN - SCOPUS:84896692853

SN - 1088-4165

VL - 18

SP - 1

EP - 14

JO - Representation Theory

JF - Representation Theory

IS - 1

ER -