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Quasi-exceptional sets and equivariant coherent sheaves on the nilpotent cone


Author: Roman Bezrukavnikov
Journal: Represent. Theory 7 (2003), 1-18
MSC (2000): Primary 20G99
DOI: https://doi.org/10.1090/S1088-4165-03-00158-4
Published electronically: January 9, 2003
MathSciNet review: 1973365
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Abstract: A certain $t$-structure on the derived category of equivariant coherent sheaves on the nil-cone of a simple complex algebraic group is introduced by the author in the paper Perverse coherent sheaves (the so-called perverse $t$-structure corresponding to the middle perversity). In the present note we show that the same $t$-structure can be obtained from a natural quasi-exceptional set generating this derived category. As a consequence we obtain a bijection between the sets of dominant weights and pairs consisting of a nilpotent orbit, and an irreducible representation of the centralizer of this element, conjectured by Lusztig and Vogan (and obtained by other means by the author in the paper On tensor categories attached to cells in affine Weyl groups, to be published).


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Additional Information

Roman Bezrukavnikov
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: bezrukav@math.northwestern.edu

DOI: https://doi.org/10.1090/S1088-4165-03-00158-4
Received by editor(s): February 15, 2002
Received by editor(s) in revised form: July 31, 2002
Published electronically: January 9, 2003
Additional Notes: The author is supported by the NSF grant DMS0071967, and by the Clay Mathematical Institute
Article copyright: © Copyright 2003 American Mathematical Society