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

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arxiv 2011.10962 v2 pith:C3HYACL7 submitted 2020-11-22 math.RT math.AG

Taiwang Deng , Bin Xu This is my paper · ORCID
classification math.RTmath.AG
keywords conjecturecharacteristiccyclestypebasiscasequiversemi-canonical
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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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