The metaplectic Casselman-Shalika formula. (English) Zbl 1338.22009
In the context of Weyl multiple Dirichlet series, G. Chinta and O. Offen have given explicit expressions for spherical Whittaker function for metaplectic covers of \(\mathrm{GL}_n(F)\) for a nonarchimedian local field \(F\), see [Am. J. Math. 135, No. 2, 403–441 (2013; Zbl 1294.22012)]. This generalizes a classical formula by Casselman and Shalika.
In the present paper, their technique is generalized to give a Casselman-Shalika formula for metaplectic covers of all unramified groups.
In the present paper, their technique is generalized to give a Casselman-Shalika formula for metaplectic covers of all unramified groups.
Reviewer: Anton Deitmar (Tübingen)
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
| 11F68 | Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series |
| 22E35 | Analysis on \(p\)-adic Lie groups |
| 33C15 | Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\) |
Citations:
Zbl 1294.22012References:
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