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Nilpotent Conjugacy Classes in $p$-adic Lie Algebras: The Odd Orthogonal Case

Published online by Cambridge University Press:  20 November 2018

Jyotsna Mainkar Diwadkar
Jyotsna Mainkar Diwadkar*
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A. e-mail: diwadkar@pitt.edu
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Abstract

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We will study the following question: Are nilpotent conjugacy classes of reductive Lie algebras over $p$-adic fields definable? By definable, we mean definable by a formula in Pas's language. In this language, there are no field extensions and no uniformisers. Using Waldspurger's parametrization, we answer in the affirmative in the case of special orthogonal Lie algebras $\mathfrak{s}\mathfrak{o}\left( n \right)$ for $n$ odd, over $p$-adic fields.

Keywords

17B1003C60
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 1 , 01 February 2008 , pp. 88 - 108
Copyright
Copyright © Canadian Mathematical Society 2008

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