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Weyl Group Multiple Dirichlet Series by Ben Brubaker, Daniel Bump, Solomon Friedberg

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Chapter Twenty

Crystals and p-adic Integration

In many cases, integrations of representation theoretic import over the maximal unipotent subgroup of a p-adic group can be replaced by a sum over Kashiwara’s crystal Image(∞). Partly motivated by the crystal description presented in Chapter 2 of this book, this perspective was advocated by Bump and Nakasuji in [21]. Later work by McNamara [65] and Kim and Lee [50] extended this philosophy yet further. Indeed, McNamara shows that the computation of the metaplectic Whittaker function is initially given as a sum over (∞), which, upon closer examination, degenerates to the sum over presented in Chapter 2 ...

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