Character D-modules via Drinfeld center of Harish-Chandra bimodules
Name
Bezrukavnikov_Character D-Modules.pdf
Size
334.24 KB
Format
Adobe PDF
Checksum (MD5)
1dd36c927d813711e9d3b788ef3fda7a
Author(s)
Bezrukavnikov, Roman
Finkelberg, Michael
Ostrik, Viktor
Date Issued
September 2011
Journal
Inventiones Mathematicae
Publisher
Springer-Verlag
Citation
Bezrukavnikov, Roman, Michael Finkelberg, and Victor Ostrik. “Character D-modules via Drinfeld Center of Harish-Chandra Bimodules.” Inventiones mathematicae (2011): n. pag. Web. 4 May 2012. © 2011 Springer-Verlag
Version
Author's final manuscript
Abstract
The category of character D-modules is realized as Drinfeld center of the abelian monoidal category of Harish-Chandra bimodules. Tensor product of Harish-Chandra bimodules is related to convolution of D-modules via the long intertwining functor (Radon transform) by a result of Beilinson and Ginzburg (Represent. Theory 3, 1–31, 1999). Exactness property of the long intertwining functor on a cell subquotient of the Harish-Chandra bimodules category shows that the truncated convolution category of Lusztig (Adv. Math. 129, 85–98, 1997) can be realized as a subquotient of the category of Harish-Chandra bimodules. Together with the description of the truncated convolution category (Bezrukavnikov et al. in Isr. J. Math. 170, 207–234, 2009) this allows us to derive (under a mild technical assumption) a classification of irreducible character sheaves over ℂ obtained by Lusztig by a different method.
We also give a simple description for the top cohomology of convolution of character sheaves over ℂ in a given cell modulo smaller cells and relate the so-called Harish-Chandra functor to Verdier specialization in the De Concini–Procesi compactification.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00222-011-0354-3
