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The characteristic cycles and semi-canonical bases on type A quiver variety

Taiwang Deng Yau Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing, 100084, China Bin Xu Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University, Beijing, China

Representation Theory Algebraic Geometry mathscidoc:2206.30001

Journal of Algebra, 598, (15), 392-444, 2022.5
In this article we study a conjecture of Geiss-Leclerc-Schröer, which is an analogue of a classical conjecture of Lusztig in the Weyl group case. It concerns the relation between canonical basis and semi-canonical basis through the characteristic cycles. We formulate an approach to this conjecture and prove it for type quiver. In the general type A case, we reduce the conjecture to show that certain nearby cycles have vanishing Euler characteristic.
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@inproceedings{taiwang2022the,
  title={The characteristic cycles and semi-canonical bases on type A quiver variety},
  author={Taiwang Deng, and Bin Xu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618160855489290404},
  booktitle={Journal of Algebra},
  volume={598},
  number={15},
  pages={392-444},
  year={2022},
}
Taiwang Deng, and Bin Xu. The characteristic cycles and semi-canonical bases on type A quiver variety. 2022. Vol. 598. In Journal of Algebra. pp.392-444. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618160855489290404.
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