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 arXiv, (Unpublished)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 arXiv, (Unpublished)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Status:Unpublished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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