Quiver varieties and crystals in symmetrizable type via modulated graphs
نویسندگان
چکیده
منابع مشابه
Combinatorial realizations of crystals via torus actions on quiver varieties
Let V (λ) be a highest-weight representation of a symmetric Kac–Moody algebra, and let B(λ) be its crystal. There is a geometric realization of B(λ) using Nakajima’s quiver varieties. In many particular cases one can also realize B(λ) by elementary combinatorial methods. Here we study a general method of extracting combinatorial realizations from the geometric picture: we use Morse theory to in...
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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...
متن کامل0 Quiver Varieties of Type A
We prove a conjecture of Nakajima describing the relation between the geometry of quiver varieties of type A and the geometry of the partial flags varieties and of the 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 Kronehei...
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We saw in lectures 7 and 8 how Lusztig’s nilpotent variety can be used to realize U−(g) and the crystal B(∞). Last week we saw how to use quiver grassmannians to realize the highest weight modules V (λ) as a quotient of U−(g), and the same construction realizes the crystals B(λ). This week we discuss a more standard approach to realizing V (λ) and B(λ), namely we will use Nakajima’s quiver vari...
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Braverman-Finkelberg [4] recently propose the geometric Satake correspondence for the affine Kac-Moody group Gaff . They conjecture that intersection cohomology sheaves on the Uhlenbeck compactification of the framed moduli space of Gcpt-instantons on R /Zr correspond to weight spaces of representations of the Langlands dual group G∨aff at level r. When G = SL(l), the Uhlenbeck compactification...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2018
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2018.v25.n1.a7