Crystals via the Affine Grassmannian

@inproceedings{Braverman2000CrystalsVT,
  title={Crystals via the Affine Grassmannian},
  author={Alexander Braverman and DENNIS GAITSGORY},
  year={2000}
}
Let G be a connected reductive group over C, and let g∨ be the Langlands dual Lie algebra. Crystals for g∨ are combinatorial objects that were introduced by M. Kashiwara (cf., e.g., [6]) as certain “combinatorial skeletons” of finite-dimensional representations of g∨. For every dominant weight λ of g∨ Kashiwara constructed a crystal B(λ) by considering the corresponding finite-dimensional representation of the quantum group Uq(g∨) and then specializing it to q = 0. Other (independent… CONTINUE READING
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