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Invariante Differentialoperatoren und die Frobenius-Zerlegung einer G-Variet"at

Ilka Agricola
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Abstract

Sei G eine zusammenhängende reduktive komplexe algebraische Gruppe, die auf einer glatten affinen komplexen Varietät M wirke, und bezeichne $\Diff[G]{M}$ die G-invarianten algebraischen Differentialoperatoren auf M. Zerlegt man den Koordinatenring $\Aff{\C}{M}$ in G-isotypische Komponenten, so zeigen wir, daß die hierbei auftretenden Vielfachheitenräume irreduzible $\Diff[G]{M}$-Moduln sind, zentralen Charakter haben und durch diesen eindeutig bestimmt sind. Anschließend beschreiben wir die analoge Zerlegung für reelle Formen und zeigen anhand einiger singulärer Beispiele, daß für nicht glatte Varietäten ähnliche Ergebnisse nicht zu erwarten sind.

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Ilka Agricola. 1999-06-14. Invariante Differentialoperatoren und die Frobenius-Zerlegung einer G-Variet"at. https://arxiv.org/abs/math/9906091

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