2020/07/09 by He, Hongyu
#11 #22E #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2007.04914
Whittaker functions of GL(n, \mathbb R) , are most known for its role in the Fourier-Whittaker expansion of cusp forms. Their behavior in the Siegel set, in large, is well-understood. In this paper, we insert into the literature some potentially useful properties of Whittaker function over the group GL(n, \mathbb R) and the mirobolic group Pn. We proved the square integrabilty of the Whittaker functions with respect to certain measures, extending a theorem of Jacquet and Shalika . For principal series representations, we gave various asymptotic bounds of smooth Whittaker functions over the whole group GL(n, \mathbb R). Due to the lack of good terminology, we use whittaker functions to refer to K-finite or smooth vectors in the Whittaker model.