We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing and provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof's conjecture on the number of finite dimensional irreducible representations for Symplectic reflection algebras associated to wreath-product groups. We use several different techniques, the two principal ones are categorical Kac-Moody actions and wall-crossing functors. We finish the paper outlining some future directions of research.

中文翻译：

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量化箭袋变体的 Etingof 猜想

我们计算量化 Nakajima quiver 变体的代数的有限维不可约模块的数量。我们得到了所有颤动和框架向量的下限，并在颤动是有限类型或仿射类型并且框架是扩展顶点处的坐标向量的情况下提供精确计数。后一种情况恰好涵盖了 Etingof 对与花圈积群相关的辛反射代数的有限维不可约表示的数量的猜想。我们使用了几种不同的技术，两个主要的技术是分类 Kac-Moody 动作和穿墙函子。我们完成了概述一些未来研究方向的论文。