We show that, on a compact symmetric space, the Lichnerowicz Laplacian acting on the space of covariant tensor fields coincides with the Casimir operator and we deduce that, on a compact semisimple Lie group, the Lichnerowicz Laplacian is the mean of the left invariant Casimir operator and the right invariant Casimir operator.
On montre que, dans un espace symétrique compact, le laplacien de Lichnerowicz agissant sur l'espace des tenseurs covariants coincide avec l'opérateur de Casimir et on déduit que, dans un groupe de Lie compact semisimple, le laplacien de Lichnerowicz est la moyenne de l'opérateur de Casimir invariant à gauche et celui invariant à droite.
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@article{CRMATH_2009__347_17-18_1061_0,
author = {Boucetta, Mohamed},
title = {The {Lichnerowicz} {Laplacian} on compact symmetric spaces},
journal = {Comptes Rendus. Math\'ematique},
pages = {1061--1066},
publisher = {Elsevier},
volume = {347},
number = {17-18},
year = {2009},
doi = {10.1016/j.crma.2009.06.019},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.06.019/}
}
TY - JOUR AU - Boucetta, Mohamed TI - The Lichnerowicz Laplacian on compact symmetric spaces JO - Comptes Rendus. Mathématique PY - 2009 SP - 1061 EP - 1066 VL - 347 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.06.019/ DO - 10.1016/j.crma.2009.06.019 LA - en ID - CRMATH_2009__347_17-18_1061_0 ER -
%0 Journal Article %A Boucetta, Mohamed %T The Lichnerowicz Laplacian on compact symmetric spaces %J Comptes Rendus. Mathématique %D 2009 %P 1061-1066 %V 347 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.06.019/ %R 10.1016/j.crma.2009.06.019 %G en %F CRMATH_2009__347_17-18_1061_0
Boucetta, Mohamed. The Lichnerowicz Laplacian on compact symmetric spaces. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1061-1066. doi : 10.1016/j.crma.2009.06.019. http://www.numdam.org/articles/10.1016/j.crma.2009.06.019/
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