Mirković–Vilonen polytopes lying in a Demazure crystal and an opposite Demazure crystal

@article{Naito2008MirkoviVilonenPL,
  title={Mirkovi{\'c}–Vilonen polytopes lying in a Demazure crystal and an opposite Demazure crystal},
  author={Satoshi Naito and Daisuke Sagaki},
  journal={Advances in Mathematics},
  year={2008},
  volume={221},
  pages={1804-1842}
}
View PDF on arXiv
6 Citations
Background Citations
2
Results Citations
1

6 Citations

Polytopal Estimate of Mirkovic-Vilonen polytopes lying in a Demazure crystal
Weight polytopes and saturation of Demazure characters
. For G a reductive group and T Ă B a maximal torus and Borel subgroup, Demazure modules are certain B -submodules, indexed by elements of the Weyl group, of the finite irreducible representations of…
Erratum to: Quiver varieties and Demazure modules
Part of the proofs of Proposition 6.1 and Theorem 8.1 relied on the statement that if w = ril · · · ri1 is a reduced expression of an element of theWeyl group and X ∈ Bw(d), then X = ẽ1 i1 · · · ẽ nl…
Relating the right key to the type A filling map and minimal defining chains
Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A
We study modules with 1-dimensional socle for preprojective algebras for type A quivers. In particular, we classify such modules, determine all homomorphisms between them, and then explain how they…
Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds
We present a new algorithm to compute initial seeds for cluster structures on categories associated with coordinate rings of open Richardson varieties. This allows us to explicitely determine seeds…

References

SHOWING 1-10 OF 54 REFERENCES
The crystal structure on the set of Mirkovic-Vilonen polytopes
Mirkovic-Vilonen cycles and polytopes
We give an explicit description of the Mirkovie-Vilonen cycles on the affine Grassmannian for arbitrary complex reductive groups. We also give a combinatorial characterization of the MV polytopes. We…
The action of a Dynkin automorphism on Mirkovic-Vilonen cycles and polytopes
We consider the action of a Dynkin automorphism σ on Mirković-Vilonen cycles and polytopes for a semisimple algebraic group G. In this paper, we get a bijection between the set of σ-invariant MV…
Mirkovic-Vilonen cycles and polytopes for a Symmetric pair
Let $G$ be a connected, simply-connected, and almost simple algebraic group, and let $\sigma$ be a Dynkin automorphism on $G$. In this paper, we get a bijection between the set of $\st$-invariant MV…
A modification of the Anderson-Mirkovic conjecture for Mirkovic-Vilonen polytopes in types B and C
Quiver varieties and Demazure modules
Using subvarieties, which we call Demazure quiver varieties, of the quiver varieties of Nakajima, we give a geometric realization of Demazure modules of Kac-Moody algebras with symmetric Cartan data.…
Résolutions de Demazure affines et formule de Casselman-Shalika géométrique
We prove a conjecture of Frenkel, Gaitsgory, Kazhdan and Vilonen, related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a a split reductive group. Our…
On Mirković-Vilonen cycles and crystal combinatorics
Let G be a complex connected reductive group and let G be its Langlands dual. Let us choose a triangular decomposition n ⊕ h ⊕ n of the Lie algebra of G. Braverman, Finkelberg and Gaitsgory show that…
Polytopes for Crystallized Demazure Modules and Extremal Vectors
Abstract We give a parametrization for crystal bases of Demazure modules as a set of lattice points in some convex polytope and we also describe explicitly the extremal vectors as solutions of some…
LS galleries, the path model, and MV cycles
We give an interpretation of the path model of a representation [18] of a complex semisimple algebraic group G in terms of the geometry of its affine Grassmannian. In this setting, the paths are…
...
...