Equivariant coherent sheaves on the exotic nilpotent cone

Details Equivariant coherent sheaves on the exotic nilpotent cone Equivariant coherent sheaves on the exotic nilpotent cone

2012-03-23

arxiv.org/abs/1203.5364v2

Mathematics

Quantum Algebra

Scientific paper

Let $G=Sp_{2n}(\mathbb{C})$, and $\mathfrak{N}$ be Kato's exotic nilpotent cone. Following techniques used by Bezrukavnikov in [5] to establish a bijection between $\Lambda^+$, the dominant weights for a simple algebraic group $H$, and $\textbf{O}$, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit, we prove an analogous statement for the exotic nilpotent cone. First we prove that dominant line bundles on the exotic Springer resolution $\widetilde{\mathfrak{N}}$ have vanishing higher cohomology, and compute their global sections using techniques of Broer. This allows to show that the direct images of these dominant line bundles constitute a quasi-exceptional set generating the category $D^b(Coh^G(\mathfrak{N}))$, and deduce that the resulting $t$-structure on $D^b(Coh^G(\mathfrak{N}))$ coincides with the perverse coherent $t$-structure. The desired result now follows from the bijection between costandard objects and simple objects in the heart of this $t$-structure on $D^b(Coh^G(\mathfrak{N}))$.

Affiliated with

Also associated with

No associations

Rating

Equivariant coherent sheaves on the exotic nilpotent cone does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equivariant coherent sheaves on the exotic nilpotent cone, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivariant coherent sheaves on the exotic nilpotent cone will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-38826