Representation Theory of Quantized Gieseker Varieties, I

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


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.


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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