The Subregular Germ of Orbital Integrals

The Subregular Germ of Orbital Integrals

by Thomas Callister Hales
     
 

ISBN-10: 0821825399

ISBN-13: 9780821825396

Pub. Date: 09/02/1992

Publisher: American Mathematical Society

Langlands theory predicts deep relationships between representations of different reductive groups over a local or global field. The trace formula attempts to reduce many such relationships to problems concerning conjugacy classes and integrals over conjugacy classes (orbital integrals) on $p$-adic groups. It is possible to reformulate these problems as ones in

Overview

Langlands theory predicts deep relationships between representations of different reductive groups over a local or global field. The trace formula attempts to reduce many such relationships to problems concerning conjugacy classes and integrals over conjugacy classes (orbital integrals) on $p$-adic groups. It is possible to reformulate these problems as ones in algebraic geometry by associating a variety $Y$ to each reductive group. Using methods of Igusa, the geometrical properties of the variety give detailed information about the asymptotic behavior of integrals over conjugacy classes. This monograph constructs the variety $Y$ and describes its geometry. As an application, the author uses the variety to give formulas for the leading terms (regular and subregular germs) in the asymptotic expansion of orbital integrals over $p$-adic fields. The final chapter shows how the properties of the variety may be used to confirm some predictions of Langlands theory on orbital integrals, Shalika germs, and endoscopy.

Product Details

ISBN-13:
9780821825396
Publisher:
American Mathematical Society
Publication date:
09/02/1992
Series:
Memoirs Series, #47
Pages:
142
Product dimensions:
7.09(w) x 10.04(h) x (d)

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