منابع مشابه
The Metaplectic Casselman-shalika Formula
This paper studies spherical Whittaker functions for central extensions of reductive groups over local fields. We follow the development of Chinta-Offen to produce a metaplectic Casselman-Shalika formula for tame covers of all unramified groups.
متن کاملA METAPLECTIC CASSELMAN-SHALIKA FORMULA FOR GLr
We provide formulas for various bases of spherical Whittaker functions on the n-fold metaplectic cover of GLr over a p-adic field and show that there is a basis of symmetric functions in the complex parameter. In addition we relate a specific spherical Whittaker function to the p-power part of the Weyl group multiple Dirichlet series for the root system of type Ar−1 constructed from nth order G...
متن کاملThe Casselman-Shalika Formula for a Distinguished Model
Unramified Whittaker functions and their analogues occur naturally in number theory as terms in the Fourier expansions of automorphic forms. Precise information about these functions is useful in many aspects of study, such as in the construction of L-functions. In this paper, the method of Casselman-Shalika is used to derive explicit values for the analogue of the unramified Whittaker function...
متن کاملAdelic Fourier - Whittaker Coefficients and the Casselman - Shalika formula
In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, in...
متن کاملCombinatorics of Casselman-shalika Formula in Type A
In the recent works of Brubaker-Bump-Friedberg, Bump-Nakasuji, and others, the product in the Casselman-Shalika formula is written as a sum over a crystal. The coefficient of each crystal element is defined using the data coming from the whole crystal graph structure. In this paper, we adopt the tableau model for the crystal and obtain the same coefficients using data from each individual table...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6597