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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
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-v2rw-4a62
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.