Journal
INVENTIONES MATHEMATICAE
Volume 223, Issue 3, Pages 1097-1226Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-020-01007-z
Keywords
Primary 16G99; Secondary 16G20; 53D20; 53D55
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Funding
- NSF [DMS-1161584, DMS-1102434]
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In this study, the number of finite dimensional irreducible modules for algebras quantizing Nakajima quiver varieties is computed. A lower bound is obtained for all quivers and framing vectors, with an exact count provided in certain cases. Different techniques, including categorical Kac-Moody actions and wall-crossing functors, are used to achieve these results.
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. We 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.
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