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Whittaker functions and Demazure characters. (English) Zbl 1472.11162

Summary: In this paper, we consider how to express an Iwahori-Whittaker function through Demazure characters. Under some interesting combinatorial conditions, we obtain an explicit formula and thereby a generalization of the Casselman-Shalika formula. Under the same conditions, we compute the transition matrix between two natural bases for the space of Iwahori fixed vectors of an induced representation of a \(p\)-adic group; this corrects a result of D. Bump and M. Nakasuji [Can. J. Math. 63, No. 6, 1238–1253 (2011; Zbl 1230.22009)].

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E50 Representations of Lie and linear algebraic groups over local fields
20F55 Reflection and Coxeter groups (group-theoretic aspects)

Citations:

Zbl 1230.22009
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References:

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