Dissertation/Thesis Abstract

Base change for the Iwahori-Hecke algebra of GL2
by Ray-Dulany, Walter Randolph, Ph.D., University of Maryland, College Park, 2010, 82; 3426424
Abstract (Summary)

Let F be a local non-Archimedean field of characteristic not equal to 2, let E/F be a finite unramified extension field, and let σ be a generator of Gal(E, F). Let f be an element of Z([special characters omitted]), the center of the Iwahori-Hecke algebra for GL 2(E), and let b be the Iwahoric base change homomorphism from Z([special characters omitted]) to Z([special characters omitted]), the center of the Iwahori-Hecke algebra for GL 2(F) [8]. This paper proves the matching of the σ-twisted orbital integral over GL2(E) of f with the orbital integral over GL 2(F) of bf. To do so, we compute the orbital and σ-twisted orbital integrals of the Bernstein functions zμ. These integrals are computed by relating them to counting problems on the set of edges in the building for SL 2. Surprisingly, the integrals are found to be somewhat independent of the conjugacy class over which one is integrating. The matching of the integrals follows from direct comparison of the results of these computations. The fundamental lemma proved here is an important ingredient in study of Shimura varieties with Iwahori level structure at a prime p [7].

Indexing (document details)
Advisor: Haines, Thomas J.
Commitee: Adams, Jeffrey, Miller, M. C., Millson, John, Tamvakis, Harry, Washington, Lawrence
School: University of Maryland, College Park
Department: Mathematics
School Location: United States -- Maryland
Source: DAI-B 71/11, Dissertation Abstracts International
Subjects: Mathematics
Keywords: Fundamental lemmas, GL2, Iwahori-Hecke algebra, Orbital integrals, Twisted orbital integrals
Publication Number: 3426424
ISBN: 978-1-124-27119-4
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