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arXiv · 2011.10962

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

Taiwang Deng·Bin Xu
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Abstract

In this article we study a conjecture of Geiss-Leclerc-Schr{\"o}er, 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 $A_2$ quiver. In general type A case, we reduce the conjecture to show that certain nearby cycles have vanishing Euler characteristic.

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Taiwang Deng, Bin Xu. 2020-11-22. The characteristic cycles and semi-canonical bases on type $A$ quiver variety. https://arxiv.org/abs/2011.10962

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