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Author ORCID Identifier
N/A
AccessType
Open Access Dissertation
Document Type
dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
Year Degree Awarded
2018
Month Degree Awarded
September
First Advisor
Ivan Mirkovic
Subject Categories
Algebra
Abstract
The irreducible components of the variety of all modules over the preprojective algebra and MV cycles both index bases of the universal enveloping algebra of the positive part of a semisimple Lie algebra canonically. To relate these two objects Baumann and Kamnitzer associate a cycle in the affine Grassmannian to a given module. It is conjectured that the ring of functions of the T-fixed point subscheme of the associated cycle is isomorphic to the cohomology ring of the quiver Grassmannian of the module. I give a proof of part of this conjecture. The relation between this conjecture and the reduceness conjecture is explained at the end.
DOI
https://doi.org/10.7275/12715994
Recommended Citation
Dong, Zhijie, "A relation between Mirkovic-Vilonen cycles and modules over preprojective algebra of Dynkin quiver of type ADE" (2018). Doctoral Dissertations. 1335.
https://doi.org/10.7275/12715994
https://scholarworks.umass.edu/dissertations_2/1335