Quantizations of conical symplectic resolutions I: local and global structure

By Tom Braden, Nicholas Proudfoot, Ben Webster. Astérisque, 2012

128 citations recorded by the source corpus.

We re-examine some topics in representation theory of Lie algebras and Springer theory in a more general context, viewing the universal enveloping algebra as an example of the section ring of a quantization of a conical symplectic resolution. While some modification from this classical context is necessary, many familiar features survive. These include a version of the Beilinson-Bernstein localization theorem, a theory of Harish-Chandra bimodules and their relationship to convolution operators on cohomology, and a discrete group action on the derived category of representations, generalizing the braid group action on category O via twisting functors. Our primary goal is to apply these results to other quantized symplectic resolutions, including quiver varieties and hypertoric varieties. This provides a new context for known results about Lie algebras, Cherednik algebras, finite W-algebras, and hypertoric enveloping algebras, while also pointing to the study of new algebras arising from more general resolutions.

Subfields: Mathematical Physics, Pulmonary and Respiratory Medicine, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/7cd79781f020bbcf315af4094539f49069d9ddb4

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In Mathematical Physics

  1. I. Losev
  2. V. Ginzburg
  3. T. Arakawa
  4. A. Premet
  5. I. Gordon
  6. Ben Webster

In Pulmonary and Respiratory Medicine

  1. I. Losev

In Radiology, Nuclear Medicine and Imaging

  1. I. Losev

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