ترغب بنشر مسار تعليمي؟ اضغط هنا

Equivariant coherent sheaves on the exotic nilpotent cone

148   0   0.0 ( 0 )
 نشر من قبل Vinoth Nandakumar
 تاريخ النشر 2012
  مجال البحث
والبحث باللغة English
 تأليف Vinoth Nandakumar




اسأل ChatGPT حول البحث

Let $G=Sp_{2n}(mathbb{C})$, and $mathfrak{N}$ be Katos 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 $D^b(Coh^G(mathfrak{N}))$.



قيم البحث

اقرأ أيضاً

154 - Martin H. Weissman 2017
When $W$ is a finite Coxeter group acting by its reflection representation on $E$, we describe the category ${mathsf{Perv}}_W(E_{mathbb C}, {mathcal{H}}_{mathbb C})$ of $W$-equivariant perverse sheaves on $E_{mathbb C}$, smooth with respect to the st ratification by reflection hyperplanes. By using Kapranov and Schechtmans recent analysis of perverse sheaves on hyperplane arrangements, we find an equivalence of categories from ${mathsf{Perv}}_W(E_{mathbb C}, {mathcal{H}}_{mathbb C})$ to a category of finite-dimensional modules over an algebra given by explicit generators and relations. We also define categories of equivariant perverse sheaves on affine buildings, e.g., $G$-equivariant perverse sheaves on the Bruhat--Tits building of a $p$-adic group $G$. In this setting, we find that a construction of Schneider and Stuhler gives equivariant perverse sheaves associated to depth zero representations.
114 - David Barnes , Danny Sugrue 2020
We develop the theory of equivariant sheaves over profinite spaces, where the group is also taken to be profinite. We construct a good notion of equivariant presheaves, with a suitable sheafification functor. Using these results on equivariant preshe aves, we give explicit constructions of products of equivariant sheaves of R-modules. We introduce an equivariant analogue of skyscraper sheaves, which allows us to show that the category of equivariant sheaves of R-modules over a profinite space has enough injectives. This paper also provides the basic theory for results by the authors on giving an algebraic model for rational G-spectra in terms of equivariant sheaves over profinite spaces. For those results, we need a notion of Weyl-G-sheaves over the space of closed subgroups of G. We show that Weyl-G-sheaves of R-modules form an abelian category, with enough injectives, that is a full subcategory of equivariant sheaves of R-modules. Moreover, we show that the inclusion functor has a right adjoint.
99 - Xinwen Zhu 2020
We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of arithmetic local Langlands parameters, including their roles played in the local-global compatibility in the Langlands program. We survey some known results as evidences of these conjectures.
346 - Paul G. Goerss 2008
The central aim of this monograph is to provide decomposition results for quasi-coherent sheaves on the moduli stack of one-dimensional formal groups. These results will be based on the geometry of the stack itself, particularly the height filtration and an analysis of the formal neighborhoods of the geometric points. The main theorems are algebraic chromatic convergence results and fracture square decompositions. There is a major technical hurdle in this story, as the moduli stack of formal groups does not have the finitness properties required of an algebraic stack as usually defined. This is not a conceptual problem, but in order to be clear on this point and to write down a self-contained narrative, I have included a great deal of discussion of the geometry of the stack itself, giving various equivalent descriptions.
139 - Andrea Jedwab , Leonid Krop 2009
We derive a formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent liftings of quantum planes. We show that the trace is equal to the quantum dimension of the module up to a nonzero scalar depending on the simple module.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا