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Homogeneity of Certain Invariant Distributions on the Lie Algebra of p-adic GLn

Published online by Cambridge University Press:  04 December 2007

Stephen Debacker
Stephen Debacker
Affiliation:
Department of Mathematics, The University of Chicago, Chicago, IL 60637, U.S.A. E-mail: debacker@math.uchicago.edu
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Abstract

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Let F be a non-Archimedean local field with ring of integers R and prime ideal $\frak p$. Suppose T is a GLn(F)-invariant distribution on ${\frak g}$=Mn(F), the Lie algebra of GLn(F). If T has support in the set of topologically nilpotent elements, then the restriction of T to the set of functions which are compactly supported and invariant under Mn($\frak p$) may be expressed as a linear combination of nilpotent orbital integrals restricted to the same set of functions.

Keywords

distributionshomogeneityLie algebrap-adic group
Type
Research Article
Information
Compositio Mathematica , Volume 124 , Issue 1 , October 2000 , pp. 11 - 16
Copyright
© 2000 Kluwer Academic Publishers