Geodesic
Nilpotent Conjugacy Classes in $p$ -adic Lie Algebras: The Odd Orthogonal Case
Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 88-108

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2008-004-6
Mots-clés : 17B10, 03C60 
Diwadkar, Jyotsna Mainkar. Nilpotent Conjugacy Classes in $p$ -adic Lie Algebras: The Odd Orthogonal Case. Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 88-108. doi: 10.4153/CJM-2008-004-6
@article{10_4153_CJM_2008_004_6,
     author = {Diwadkar, Jyotsna Mainkar},
     title = {Nilpotent {Conjugacy} {Classes} in $p$ -adic {Lie} {Algebras:} {The} {Odd} {Orthogonal} {Case}},
     journal = {Canadian journal of mathematics},
     pages = {88--108},
     year = {2008},
     volume = {60},
     number = {1},
     doi = {10.4153/CJM-2008-004-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2008-004-6/}
}
TY  - JOUR
AU  - Diwadkar, Jyotsna Mainkar
TI  - Nilpotent Conjugacy Classes in $p$ -adic Lie Algebras: The Odd Orthogonal Case
JO  - Canadian journal of mathematics
PY  - 2008
SP  - 88
EP  - 108
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2008-004-6/
DO  - 10.4153/CJM-2008-004-6
ID  - 10_4153_CJM_2008_004_6
ER  - 
%0 Journal Article
%A Diwadkar, Jyotsna Mainkar
%T Nilpotent Conjugacy Classes in $p$ -adic Lie Algebras: The Odd Orthogonal Case
%J Canadian journal of mathematics
%D 2008
%P 88-108
%V 60
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2008-004-6/
%R 10.4153/CJM-2008-004-6
%F 10_4153_CJM_2008_004_6

[1] [1] Denef, J. and Loeser, F., Definable sets, motives and p-adic integrals. J. Amer.Math. Soc. 14(2001), no. 2, 429–469. Google Scholar

[2] [2] Gordon, J.: Motivic nature of character values of depth-zero representations. Int. Math. Rev. Not 2004, no. 34, 1735–1760. Google Scholar

[3] [3] Gordon, J. and Hales, T. C., Virtual Transfer Factors arXiv:math.RT/0209001 2002. Google Scholar

[4] [4] Enderton, H. B., A mathematical introduction to logic. Second edition. Harcourt Academic Press, Burlington,MA, 2001. Google Scholar

[5] [5] Hales, T. C., Can p-adic integrals be computed? arXiv:math.RT/0205207, 2002. Google Scholar

[6] [6] Hales, T. C., Orbital integrals are motivic arXiv:math.RT/0212236, 2002. Google Scholar

[7] [7] Hodges, W. A Shorter Model Theory. Cambridge University Press, Cambridge, 1997. Google Scholar

[8] [8] Iwasawa, K.: Local Class Field Theory. Oxford University Press. New York, 1986. Google Scholar

[9] [9] O’Meara, O. T.: Introduction to Quadratic Forms. Grundlehren des Mathematischen Wissenschaften 117, Springer-Verlag, Berlin, 1963. Google Scholar

[10] [10] Pas, J.: Uniform p-adic cell decomposition and local zeta functions. J. Reine Angew.Math. 399(1989), 137–172. Google Scholar

[11] [11] Quine, W. V., Mathematical Logic. Revised edition. Harvard University Press, Cambridge, MA, 1981. Google Scholar

[12] [12] Quine, W. V., Set Theory and Its Logic. Harvard University Press, Cambridge, MA, 1963. Google Scholar

[13] [13] Repka, J.: Shalika's Germs for p-adic GL(n). I. II. Pacific J. Math. 113(1984), no. 1, 165–182. Google Scholar

[14] [14] Scharlau, W., Quadratic and Hermitian Forms. Grundlehren derMathematischenWissenschaften 270, Springer-Verlag, Berlin, 1985. Google Scholar

[15] [15] Serre, Jean-Pierre, A Course in Arithmetic. Graduate Texts in Mathematics 7, Springer-Verlag, Berlin, 1973. Google Scholar

[16] [16] Shalika, J. A., A theorem on semi-simple p-adic groups. Ann. of Math. 95(1972), 226–242. Google Scholar

[17] [17] Waldspurger, J.-L., Intégrales orbitales nilpotentes et endoscopic pour les groupes classiques non ramifiés. Astérisque no. 269, 2001 Google Scholar

Cité par Sources :