# The Mirkovic-Vilonen basis and Duistermaat-Heckman measures

@article{Baumann2019TheMB, title={The Mirkovic-Vilonen basis and Duistermaat-Heckman measures}, author={Pierre Baumann and Joel Kamnitzer and Allen Knutson}, journal={arXiv: Representation Theory}, year={2019} }

Using the geometric Satake correspondence, the Mirkovic-Vilonen cycles in the affine Grasssmannian give bases for representations of a semisimple group G . We prove that these bases are "perfect", i.e. compatible with the action of the Chevelley generators of the positive half of the Lie algebra g. We compute this action in terms of intersection multiplicities in the affine Grassmannian. We prove that these bases stitch together to a basis for the algebra C[N] of regular functions on the… Expand

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