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Representation Theory
Representation Theory
ISSN 1088-4165

 

Homological approach to the Hernandez-Leclerc construction and quiver varieties


Authors: Giovanni Cerulli Irelli, Evgeny Feigin and Markus Reineke
Journal: Represent. Theory 18 (2014), 1-14
MSC (2010): Primary 14L30, 14M15, 16G20, 18F99
Published electronically: January 13, 2014
MathSciNet review: 3149614
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Abstract: 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.


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Additional Information

Giovanni Cerulli Irelli
Affiliation: Mathematisches Institut, Universität Bonn, Bonn, Germany 53115
Email: cerulli.math@googlemail.com

Evgeny Feigin
Affiliation: Department of Mathematics, National Research University Higher School of Economics, Russia, 117312, Moscow, Vavilova str. 7 – and – Tamm Department of Theoretical Physics, Lebedev Physics Institute, Russia
Email: evgfeig@gmail.com

Markus Reineke
Affiliation: Fachbereich C - Mathematik, Bergische Universität Wuppertal, D - 42097 Wuppertal, Germany
Email: reineke@math.uni-wuppertal.de

DOI: http://dx.doi.org/10.1090/S1088-4165-2014-00449-7
PII: S 1088-4165(2014)00449-7
Received by editor(s): March 13, 2013
Received by editor(s) in revised form: October 17, 2013
Published electronically: January 13, 2014
Article copyright: © Copyright 2014 American Mathematical Society