[Les puissances extérieures de la représentation géométrique dans la cohomologie des fibres de Springer]
Soit la cohomologie de la fibre de Springer pour l'élément nilpotent e de l'algèbre de Lie simple . Soit la i-ème puissance extérieure de la représentation géométrique de W. Nous trouvons les degrés des contributions de à la représentation graduée , si e est régulier dans une sous-algèbre de Levi et satisfait à une autre condition qui est vraie si est de type A, B, ou C. Ce résultat démontre partiellement une conjecture de Lehrer et Shoji.
Let be the cohomology of the Springer fibre for the nilpotent element e in a simple Lie algebra . Let denote the ith exterior power of the reflection representation of W. We determine the degrees in which occurs in the graded representation , under the assumption that e is regular in a Levi subalgebra and satisfies a certain extra condition which holds automatically if is of type A, B, or C. This partially verifies a conjecture of Lehrer and Shoji.
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@article{CRMATH_2010__348_19-20_1055_0,
author = {Henderson, Anthony},
title = {Exterior powers of the reflection representation in the cohomology of {Springer} fibres},
journal = {Comptes Rendus. Math\'ematique},
pages = {1055--1058},
publisher = {Elsevier},
volume = {348},
number = {19-20},
year = {2010},
doi = {10.1016/j.crma.2010.09.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.09.015/}
}
TY - JOUR AU - Henderson, Anthony TI - Exterior powers of the reflection representation in the cohomology of Springer fibres JO - Comptes Rendus. Mathématique PY - 2010 SP - 1055 EP - 1058 VL - 348 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.09.015/ DO - 10.1016/j.crma.2010.09.015 LA - en ID - CRMATH_2010__348_19-20_1055_0 ER -
%0 Journal Article %A Henderson, Anthony %T Exterior powers of the reflection representation in the cohomology of Springer fibres %J Comptes Rendus. Mathématique %D 2010 %P 1055-1058 %V 348 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.09.015/ %R 10.1016/j.crma.2010.09.015 %G en %F CRMATH_2010__348_19-20_1055_0
Henderson, Anthony. Exterior powers of the reflection representation in the cohomology of Springer fibres. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1055-1058. doi : 10.1016/j.crma.2010.09.015. http://www.numdam.org/articles/10.1016/j.crma.2010.09.015/
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