Lecture 1: Nakajima Quiver Varieties
نویسنده
چکیده
Recall that an algebraic group G is called (linearly) reductive if any its rational (i.e., algebraic) representation is completely reducible. The finite groups, the group GLn and the products GLn1 × . . .GLnk are reductive. Below G denotes a reductive algebraic group and X is an affine algebraic variety equipped with an (algebraic) action of G. Results explained below in this section can be found in [PV].
منابع مشابه
Kac conjecture from Nakajima quiver varieties
We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a a certain weight in the corresponding Kac-Moody algebra, whic...
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We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the WeylKac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which w...
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We prove a conjecture of Nakajima describing the relation between the geometry of quiver varieties of type A and the geometry of partial flags varieties and nilpotent variety. The kind of quiver varieties we are interested in, have been introduced by Nakajima as a generalization of the description of the moduli space of anti-self-dual connections on ALE spaces constructed by Kroneheimer and Nak...
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