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arXiv · 1802.01792

A relation between Mirkovi\'c-Vilonen cycles and modules over preprojective algebra of Dynkin quiver of type ADE

Zhijie Dong
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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 for 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. Given this conjecture, I give a proof of the reduceness conjecture.

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BibTeXRIS

Zhijie Dong. 2018-02-06. A relation between Mirkovi\'c-Vilonen cycles and modules over preprojective algebra of Dynkin quiver of type ADE. https://arxiv.org/abs/1802.01792

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