منابع مشابه
Preprojective Algebras and Mv Polytopes
The purpose of this paper is to apply the theory of MV polytopes to the study of components of Lusztig’s nilpotent varieties. Along the way, we introduce reflection functors for modules over the non-deformed preprojective algebra of a quiver.
متن کاملGeneralisations of Preprojective algebras
In this thesis, we investigate two ways of generalising the preprojective algebra. First, we introduce the multiplicative preprojective algebra, Λ(Q), which is a multiplicative analogue of the deformed preprojective algebra, introduced by Crawley-Boevey and Holland. The special case q = 1 is the undeformed multiplicative preprojective algebra, which is an analogue of the ordinary (undeformed) p...
متن کاملMv - Cycles and Mv - Polytopes in Type A
We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirkovi´c and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to th...
متن کاملRank 2 Affine Mv Polytopes
We give a realization of the crystal B(−∞) for ̂ sl2 using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito’s characterization of B(−∞), in terms of the ∗ involution. The polygons we use have combinatorial properties suggesting they are the ̂ sl2 analogues of the Mirković-Vilonen polytopes defined by Anderson and the third author in finite type. ...
متن کاملMv-polytopes via Affine Buildings
For an algebraic group G, Anderson originally defined the notion of MV-polytopes in [And03], images of MV-cycles, defined in [MV07], under the moment map of the corresponding affine Grassmannian. It was shown by Kamnitzer in [Kam07] and [Kam05] that these polytopes can be described via tropical relations and give rise to a crystal structure on the set of MV-cycles. Another crystal structure can...
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ژورنال
عنوان ژورنال: Representation Theory of the American Mathematical Society
سال: 2012
ISSN: 1088-4165
DOI: 10.1090/s1088-4165-2012-00413-7