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Localization theorems for quantized symplectic resolutions

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arxiv 2103.11193 v1 pith:W5NQ2RUM submitted 2021-03-20 math.RT math.AG

classification math.RTmath.AG
keywords localizationtheoremsestablishfunctorglobalresolutionssectionsymplectic
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abstract

The goal of this paper is to establish Beilinson-Bernstein type localization theorems for quantizations of some conical symplectic resolutions. We prove the full localization theorems for finite and affine type A Nakajima quiver varieties. The proof is based on two partial results that hold in more general situations. First, we establish an exactness result for global section functor if there is a tilting generator that has a rank 1 summand. Second, we examine when the global section functor restricts to an equivalence between categories $\mathcal{O}$.

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  1. Category $\mathcal{O}$ and asymptotic characters

    math.RT 2025-07 accept novelty 7.0 of 10

    The asymptotic character of a module in category O for truncated shifted Yangians equals the bar-character of its KLR module, giving a weak change-of-basis formula between the dual canonical and MV bases.

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