Point stabilisers for the enhanced and exotic nilpotent cones

Sun, Michael

doi:10.1515/jgt.2010.080

Cited by 3 publications

(1 citation statement)

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“…The enhanced nilpotent cone is defined as V × N (V ); it admits a diagonal action of GL(V ). This action has been examined in detail by several authors including Achar-Henderson [1], Travkin [22], Mautner [16] and Sun [21]. In particular the GL(V )-orbits in V × N (V ) are enumerated; it was shown by Achar-Henderson and Travkin that the orbits are naturally in bijection with bi-partitions of dim V .…”

Section: Introductionmentioning

confidence: 99%

The (cyclic) enhanced nilpotent cone via quiver representations

Bellamy

Boos

2018

manuscripta math.

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The GL(V )-orbits in the enhanced nilpotent cone V × N (V ) are (essentially) in bijection with the orbits of a certain parabolic P ⊆ GL(V ) (the mirabolic subgroup) in the nilpotent cone N (V ). We give a new parameterization of the orbits in the enhanced nilpotent cone, in terms of representations of the underlying quiver. This parameterization generalizes naturally to the enhanced cyclic nilpotent cone. Our parameterizations are different to the previous ones that have appeared in the literature. Explicit translations between the different parametrizations are given.

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Section: Introductionmentioning

confidence: 99%

The (cyclic) enhanced nilpotent cone via quiver representations

Bellamy

Boos

2018

manuscripta math.

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Affine pavings and the enhanced nilpotent cone

Mautner

2016

Proc. Amer. Math. Soc.

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Equivariant coherent sheaves on the exotic nilpotent cone

Nandakumar

2013

Represent. Theory

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Abstract. Let G = Sp 2n (C), and N be Kato's exotic nilpotent cone. Following techniques used by Bezrukavnikov in 2003 to establish a bijection between Λ + , the dominant weights for an arbitrary simple algebraic group H, and 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 N have vanishing higher cohomology, and compute their global sections using techniques of Broer. This allows us to show that the direct images of these dominant line bundles constitute a quasi-exceptional set generating the category D b (Coh G (N)), and deduce that the resulting t-structure on D b (Coh G (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 the t-structure on D b (Coh G (N)). Contents

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Point stabilisers for the enhanced and exotic nilpotent cones

Cited by 3 publications

References 6 publications

The (cyclic) enhanced nilpotent cone via quiver representations

The (cyclic) enhanced nilpotent cone via quiver representations

Affine pavings and the enhanced nilpotent cone

Equivariant coherent sheaves on the exotic nilpotent cone

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