Quasiexceptional sets and equivariant coherent sheaves on the nilpotent cone
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 Represent. Theory 7 (2003), 118 Request permission
Abstract:
A certain $t$structure on the derived category of equivariant coherent sheaves on the nilcone of a simple complex algebraic group is introduced by the author in the paper Perverse coherent sheaves (the socalled 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 quasiexceptional 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).References

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Additional Information
 Roman Bezrukavnikov
 Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
 MR Author ID: 347192
 Email: bezrukav@math.northwestern.edu
 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
 © Copyright 2003 American Mathematical Society
 Journal: Represent. Theory 7 (2003), 118
 MSC (2000): Primary 20G99
 DOI: https://doi.org/10.1090/S1088416503001584
 MathSciNet review: 1973365