# Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A

@article{Kamnitzer2011ModulesW1, title={Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A}, author={Joel Kamnitzer and Chandrika Sadanand}, journal={arXiv: Representation Theory}, year={2011}, pages={61-72} }

We study modules with 1-dimensional socle for preprojective algebras for type A quivers. In particular, we classify such modules, determine all homomorphisms between them, and then explain how they may be used to describe the components of Lusztig quiver varieties.

## 4 Citations

Preprojective algebras and MV polytopes

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The purpose of this paper is to apply the theory of MV polytopes to the study of components of Lusztig's nilpotent varieties. Along the way, we introduce reflection functors for modules over the…

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This is an REU paper written for the University of Chicago REU, summer 2017. The main purpose of this note is to collect some of the many combinatorial models for MV cycles that exist in the…

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In the current paper, we give a quiver theoretical interpretation of Mirkovi\'c-Vilonen polytopes in type $A_n$. As a by-product, we give a new proof of the Anderson-Mirkovi\'c conjecture which…

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Comparing two perfect bases Anne Dranowski Doctor of Philosophy Graduate Department of Mathematics University of Toronto 2020 We study a class of varieties which generalize the classical orbital…

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