Représentations irréductibles de certaines algèbres d'opérateurs différentiels

Details Représentations irréductibles de certaines algèbres d'opérateurs différentiels Représentations irréductibles de certaines algèbres d'opérateurs différentiels

2010-01-23

arxiv.org/abs/1001.4204v1

Mathematics

Representation Theory

Scientific paper

For a projective variety $X$ and a line bundle $L$ over $X$, one considers the $L-$twisted global differential operator algebra $\call{D}_L(X)$ which naturally operates on the space of global sections $H^0(X,L)$. In the case where $X$ is the wonderful compactification of the group $\mathrm{PGL}_3$, one proves that the space $H^0(X,L)$ is an irreducible representation of the algebra $\call{D}_L(X)$ or zero. For that, one introduces a $2-$order differential operator which is defined over whole $X$ but which does not arise from the infinitesimal action of the automorphism group $\mathrm{Aut}(X)$.

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