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

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

2001-02-06

arxiv.org/abs/math/0102039v1

Mathematics

Representation Theory

17 pages

Scientific paper

In math.AG/0005152 a certain $t$-structure on the derived category of equivariant coherent sheaves on the nil-cone of a simple complex algebraic group was introduced (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 in math.RT/0010089).

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