[Les puissances extérieures de la représentation géométrique dans la cohomologie des fibres de Springer]
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.
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.
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Henderson, Anthony 1
@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},
year = {2010},
publisher = {Elsevier},
volume = {348},
number = {19-20},
doi = {10.1016/j.crma.2010.09.015},
language = {en},
url = {https://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 - https://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 https://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
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