Abstract
We realize the non-split Bessel model of Novodvorsky and Piatetski-Shapiro in [22] as a generalized Gelfand-Graev representation of GSp(4), as suggested by Kawanaka in [17]. With uniqueness of the model already established in [22], we establish existence of a Bessel model for unramified principal series representations. We then connect the Iwahori-fixed vectors in the Bessel model to a linear character of the Hecke algebra of GSp(4) following the method outlined more generally in [3]. We use this connection to calculate the image of Iwahori-fixed vectors of unramified principal series in the model, and ultimately provide an explicit alternator expression for the spherical vector in the model. We show that the resulting alternator expression matches previous results of Bump, Friedberg, and Furusawa in [6]. We extend all results to GSp(2n), under the assumption that the aforementioned uniqueness property of the model holds for n > 2.
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