Gindikin-Karpelevich Finiteness for Local Kac-Moody Groups

  • Author / Creator
    Ali, Abid
  • One of the main difficulties in extending Macdonald’s theory of spherical functions from p-adic Chevalley groups to p-adic Kac-Moody groups is the absence of Haar measure in the infinite dimensional case. Related to this problem is the question of how to generalize the integral defining Harish-Chandra’s c-function to the p-adic Kac-Moody setting. Finding answers to these questions is the key objective of this thesis.

    Our main results, proven in the setting of p-adic Kac-Moody groups, are the finiteness of formal analogues of the spherical function (Spherical Finiteness), the c-function (Gindikin-Karpelevich Finiteness), and a formal analogue of Harish-
    Chandra’s limit (Approximation Theorem) relating spherical and c-function.
    These results have been proven by A. Braverman, H. Garland, D. Kazhdan and M. Patnaik for untwisted affine Kac-Moody groups using algebraic and representation theoretic techniques. In this thesis, we prove these results for p-adic Kac-Moody groups by using a method motivated by Braverman et. al. but distinct even in the affine case.

  • Subjects / Keywords
  • Graduation date
    Fall 2019
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
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