Surprising properties of centralisers in classical Lie algebras

Oksana Yakimova[1]

  • [1] Universität Erlangen-Nürnberg Mathematisches Institut Bismarckstrasse 1 1/2 91054 Erlangen (Germany)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 3, page 903-935
  • ISSN: 0373-0956

Abstract

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Let 𝔤 be a classical Lie algebra, i.e., either 𝔤𝔩 n , 𝔰𝔭 n , or 𝔰𝔬 n and let e be a nilpotent element of 𝔤 . We study various properties of the centralisers 𝔤 e . The first four sections deal with rather elementary questions, like the centre of 𝔤 e , commuting varieties associated with 𝔤 e , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on 𝔤 e * and symmetric invariants of 𝔤 e .

How to cite

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Yakimova, Oksana. "Surprising properties of centralisers in classical Lie algebras." Annales de l’institut Fourier 59.3 (2009): 903-935. <http://eudml.org/doc/10423>.

@article{Yakimova2009,
abstract = {Let $\mathfrak\{g\}$ be a classical Lie algebra, i.e., either $\mathfrak\{gl\}_n$, $\mathfrak\{sp\}_n$, or $\mathfrak\{so\}_n$ and let $e$ be a nilpotent element of $\mathfrak\{g\}$. We study various properties of the centralisers $\mathfrak\{g\}_e$. The first four sections deal with rather elementary questions, like the centre of $\mathfrak\{g\}_e$, commuting varieties associated with $\mathfrak\{g\}_e$, or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on $\mathfrak\{g\}_e^*$ and symmetric invariants of $\mathfrak\{g\}_e$.},
affiliation = {Universität Erlangen-Nürnberg Mathematisches Institut Bismarckstrasse 1 1/2 91054 Erlangen (Germany)},
author = {Yakimova, Oksana},
journal = {Annales de l’institut Fourier},
keywords = {Nilpotent orbits; centralisers; symmetric invariants},
language = {eng},
number = {3},
pages = {903-935},
publisher = {Association des Annales de l’institut Fourier},
title = {Surprising properties of centralisers in classical Lie algebras},
url = {http://eudml.org/doc/10423},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Yakimova, Oksana
TI - Surprising properties of centralisers in classical Lie algebras
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 3
SP - 903
EP - 935
AB - Let $\mathfrak{g}$ be a classical Lie algebra, i.e., either $\mathfrak{gl}_n$, $\mathfrak{sp}_n$, or $\mathfrak{so}_n$ and let $e$ be a nilpotent element of $\mathfrak{g}$. We study various properties of the centralisers $\mathfrak{g}_e$. The first four sections deal with rather elementary questions, like the centre of $\mathfrak{g}_e$, commuting varieties associated with $\mathfrak{g}_e$, or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on $\mathfrak{g}_e^*$ and symmetric invariants of $\mathfrak{g}_e$.
LA - eng
KW - Nilpotent orbits; centralisers; symmetric invariants
UR - http://eudml.org/doc/10423
ER -

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