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

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Chapter Four

Whittaker Functions

Weyl group multiple Dirichlet series are expected to be Whittaker coefficients of metaplectic Eisenstein series. The fact that Whittaker coefficients of Eisenstein series reduce to the crystal description that we gave in Chapter 2 is proved for Type A. In a classical setting, this was established by Brubaker, Bump, and Friedberg [13]. Alternatively, on the adele group, the corresponding local computation reduces to the evaluation of a type of p-adic integral. These were considered by McNamara [65], who reduced the integrals to sums over crystals by a very interesting method. A full treatment of this topic is outside the scope of this work, but we will introduce this subject by considering the case where n = 1. ...

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