The unramified principal series of p-adic groups : the Bessel function
Author(s)DeFranco, Mario A. (Mario Anthony)
Massachusetts Institute of Technology. Department of Mathematics.
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Let G be a connected reductive group with a split maximal torus defined over a nonarchimedean local field. I evaluate a matrix coefficient of the unramified principal series of G known as the "Bessel function" at torus elements of dominant coweight. I show that the Bessel function shares many properties with the Macdonald spherical function of G, in particular the properties described in Casselman's 1980 evaluation of that function. The analogy I demonstrate between the Bessel and Macdonald spherical functions extends to an analogy between the spherical Whittaker function, evaluated by Casselman and Shalika in 1980, and a previously unstudied matrix coefficient.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.Cataloged from PDF version of thesis.Includes bibliographical references (pages 99-101).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology