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Let ΩῩ denote the sheaf of differentials on the smooth irreducible projective curve Ῡ (see [Har, Chapter II, §8] for the definition). As dim Ῡ = 1, it coincides with the canonical sheaf and is locally free of rank 1 (see [Har, Chapter II, Theorem 8.15]). The \({\mathbb{F}}\) -vector space of global sections Γ(Ῡ, ΩῩ) inherits an action of G and it is the aim of this chapter to decompose it as a direct sum of indecomposable modules (see Theorem 11.2.2: it is a recent result of Lucas and Köck [LuKo]).

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Canonical Representation Associated with Ῡ

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  • 发表日期：

    2026年

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  • Cédric Bonnafé

摘要

Let ΩῩ denote the sheaf of differentials on the smooth irreducible projective curve Ῡ (see [Har, Chapter II, §8] for the definition). As dim Ῡ = 1, it coincides with the canonical sheaf and is locally free of rank 1 (see [Har, Chapter II, Theorem 8.15]). The \({\mathbb{F}}\) -vector space of global sections Γ(Ῡ, ΩῩ) inherits an action of G and it is the aim of this chapter to decompose it as a direct sum of indecomposable modules (see Theorem 11.2.2: it is a recent result of Lucas and Köck [LuKo]).