Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Kloosterman sums for Chevalley groups


Author: Romuald Dąbrowski
Journal: Trans. Amer. Math. Soc. 337 (1993), 757-769
MSC: Primary 11L05; Secondary 20G05
MathSciNet review: 1102221
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A generalization of Kloosterman sums to a simply connected Chevalley group $ G$ is discussed. These sums are parameterized by pairs $ (w,t)$ where $ w$ is an element of the Weyl group of $ G$ and $ t$ is an element of a $ {\mathbf{Q}}$-split torus in $ G$. The $ SL(2,{\mathbf{Q}})$-Kloosterman sums coincide with the classical Kloosterman sums and $ SL(r,{\mathbf{Q}})$-Kloosterman sums, $ r \geq 3$, coincide with the sums introduced in [B-F-G,F,S]. Algebraic properties of the sums are proved by root system methods. In particular an explicit decomposition of a general Kloosterman sum over $ {\mathbf{Q}}$ into the product of local $ p$-adic factors is obtained. Using this factorization one can show that the Kloosterman sums corresponding to a toral element, which acts trivially on the highest weight space of a fundamental irreducible representation, splits into a product of Kloosterman sums for Chevalley groups of lower rank.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 11L05, 20G05

Retrieve articles in all journals with MSC: 11L05, 20G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1102221-2
PII: S 0002-9947(1993)1102221-2
Article copyright: © Copyright 1993 American Mathematical Society