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

Abstract

A certain t 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 t -structure corresponding to the middle perversity). In the present note we show that the same t 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).