An observation on highest weight crystals
نویسندگان
چکیده
منابع مشابه
An Observation on Highest Weight Crystals
As shown in the paper of Stembridge [Ste03], crystal graphs can be characterized by their local behavior. In this paper, we observe that a certain local property on crystals forces a more global property. In type A, this statement says that if a node has a single parent and single grandparent, then there is a unique walk from the highest weight node to it. In other classical types, there is a s...
متن کاملLecture 10: Highest Weight Crystals from Quiver Varieties
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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We provide several equivalent descriptions of a highest weight category using recollements of abelian categories. Also, we explain the connection between sequences of standard and exceptional objects.
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We will now turn to the problem of classifying and constructing all finitedimensional representations of a complex semi-simple Lie algebra (or, equivalently, of a compact Lie group). It turns out that such representations can be characterized by their “highest-weight”. The first method we’ll consider is purely Lie-algebraic, it begins by constructing a universal representation with a given high...
متن کاملPolyhedral Realization of the Highest Weight Crystals for Generalized Kac-moody Algebras
In this paper, we give a polyhedral realization of the highest weight crystals B(λ) associated with the highest weight modules V (λ) for the generalized Kac-Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac-Moody algebras of ranks 2, 3, and Monster algebras.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2007.05.021