Whittaker functions and Demazure characters
  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 generalizes a result of Bump--Nakasuji. 
Kyu-Hwan Lee, Cristian Lenart, Dongwen Liu, Dinakar Muthiah, Anna   Pusk\'as
math.NT math.RT