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Representation Theory of Quantized Gieseker Varieties, I

  • Ivan Losev
Chapter
Part of the Progress in Mathematics book series (PM, volume 326)

Abstract

We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite-dimensional representations for all parameters and categories O for special values of parameters. We find the values of parameters, where the quantizations have finite homological dimension, and we establish the abelian localization theorem.We classify two-sided ideals. Finally, we determine the annihilators of the irreducible objects in categories O for some special choices of one-parameter subgroups.

Keywords

Gieseker varieties quantizations categories O localization theorems two-sided ideals 

Mathematics Subject Classification (2010):

Primary 16G99 Secondary 16G20 53D20 53D55 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ivan Losev
    • 1
    • 2
  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.International Laboratory of Representation theory and Mathematical Physics, NRU-HSEMoscowRussia

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