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

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Chapter Five

Tokuyama’s Theorem

Let z = diag(z1, · · · , zr+1) be an element of the group Image(Image), which is the diagonal subgroup of GLr+1(Image). In the application to the Casselman-Shalika formula we will take the zi to be the Langlands parameters. (In terms of the si the zi are determined by the conditions that Π zi = 1 and zi/zi+1 = Image.)

Let us write the Weyl ...

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