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

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Compositio Mathematica

Abstract

Let F be a non-Archimedean local field with ring of integers R and prime ideal \(\wp \). Suppose T is a GL n (F)-invariant distribution on \({\mathfrak{g}}\)=M n (F), the Lie algebra of GL n (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 M n (\(\wp \)) may be expressed as a linear combination of nilpotent orbital integrals restricted to the same set of functions.

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  1. Department of Mathematics, The University of Chicago, Chicago, IL, 60637, U.S.A.

    Stephen Debacker

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  1. Stephen Debacker
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Debacker, S. Homogeneity of Certain Invariant Distributions on the Lie Algebra of p-adic GLn . Compositio Mathematica 124, 11–16 (2000). https://doi.org/10.1023/A:1002479505894

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