Categorical cell decomposition of quantized symplectic algebraic varieties

Bellamy, G. , Dodd, C., McGerty, K. and Nevins, T. (2013) Categorical cell decomposition of quantized symplectic algebraic varieties. arXiv, (Unpublished)

Bellamy, G. , Dodd, C., McGerty, K. and Nevins, T. (2013) Categorical cell decomposition of quantized symplectic algebraic varieties. arXiv, (Unpublished)

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Abstract

We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the Bialynicki-Birula stratification of a variety with an action of the multiplicative group. The resulting categorical cell decomposition provides an algebro-geometric parallel to the structure of Fukaya categories of Weinstein manifolds. From it, we derive concrete consequences for invariants such as K-theory and Hochschild homology of module categories of interest in geometric representation theory.

Item Type:Articles
Status:Unpublished
Refereed:No
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G., Dodd, C., McGerty, K., and Nevins, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:arXiv
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