On simple Igusa local zeta functions
Author:
Roland Martin
Journal:
Electron. Res. Announc. Amer. Math. Soc. 1 (1995), 108-111
MSC (1991):
Primary 11D79
DOI:
https://doi.org/10.1090/S1079-6762-95-03003-4
MathSciNet review:
1369641
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Abstract: The objective of this announcement is the statement of some recent results on the classification of generalized Igusa local zeta functions associated to irreducible matrix groups. The definition of a simple Igusa local zeta function will motivate a complete classification of certain generalized Igusa local zeta functions associated to simply connected simple Chevalley groups. In addition to the novelty of these results are the various methods used in their proof. These methods include use of the concept of canonical basis from quantum group theory and a formula expressing Serre’s canonical measure $\mu _{c}$ in terms of a suitably normalized Haar measure $\mu$ and density function $\Phi$. The relevance of these results in the general theory of Igusa local zeta functions is also discussed.
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Additional Information
Roland Martin
Affiliation:
Department of Mathematics, United States Naval Academy, Annapolis, MD 21114
Email:
rem@sma.usna.navy.mil
Keywords:
Local zeta functions,
canonical bases
Received by editor(s):
September 23, 1995
Communicated by:
David Kazhdan
Article copyright:
© Copyright 1995
American Mathematical Society
