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

Published:2008-02-01
Printed: Feb 2008
• Jyotsna Mainkar Diwadkar
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Abstract

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 $\mathfrak{so}(n)$ for $n$ odd, over $p$-adic fields.
 MSC Classifications: 17B10 - Representations, algebraic theory (weights) 03C60 - Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]

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