Toric Degenerations

: Together with Jihyeon Jessie Yang, we resurrected an old idea of Raoul Bott for using large torus actions to construct canonical bases for unitary representations of compact Lie groups. Our methods are complex analytic. We apply them to families of Bott-Samelson manifolds parametrized by C n . This application requires the vanishing of higher cohomology of sheaves of holomorphic sections of certain line bundles over

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