We study the generalized Whittaker models for G = GSp(2,R) associated with indefinite binary quadratic forms when they arise from two standard representations of G: (i) a generalized principal series representation induced from the non-Siegel maximal parabolic subgroup and (ii) a (limit of) large discrete series representation. We prove the uniqueness of such models with moderate growth property. Moreover we express the values of the corresponding generalized Whittaker functions on a one-parameter subgroup of G in terms of the Meijer G-functions.
"Generalized Whittaker functions on GSp(2,R) associated with indefinite quadratic forms." J. Math. Soc. Japan 63 (4) 1203 - 1262, October, 2011. https://doi.org/10.2969/jmsj/06341203