Point stabilisers for the enhanced and exotic nilpotent cones
نویسندگان
چکیده
منابع مشابه
Orbits in the Enhanced and Exotic Nilpotent Cones
We give a semi-direct product decomposition of the point stabilisers for the enhanced and exotic nilpotent cones. In particular, we arrive at formulas for the number of points in each orbit over a finite field. This is in accordance with a conjecture of Achar-Henderson. Introduction In the theory of algebraic groups, we find that there is much insight to be gained from studying the nilpotent co...
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This paper is a sequel to [K]. Let G be a complex symplectic group. In [K], we constructed a certain G-variety N = N1, which we call the (1-) exotic nilpotent cone. In this paper, we study the set of G-orbits of the variety N. It turns out that the variety N gives a variant of the Springer correspondence for the Weyl group of type C, but shares a similar flavor with that of type A case. (I.e. t...
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Let G be a complex symplectic group. We construct a certain Gvariety N, which shares many nice properties with the nilpotent cone of G. For example, it is normal, has finitely many G-orbits, and admits a G-equivariant resolution of singularity in a similar way to the Springer resolution. Our new G-variety admits an action of G× C × C instead of the G×C-action on the nilpotent cone. This enables...
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Let G = Sp(2n) be the symplectic group over Z. We present a certain kind of deformation of the nilpotent cone of G with G-action. This enables us to make direct links between the Springer correspondence of sp 2n over C, that over characteristic two, and our exotic Springer correspondence. As a by-product, we obtain a complete description of our exotic Springer correspondence.
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2011
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2010.080