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- W2246382146 abstract "Let $G$ be a finite subgroup of the linear group of a finite-dimensional complex vector $V$, $B={operatorname S}(V)$ be the symmetric algebra, ${mathcal D}=mathcal D^G_B$ the ring of $G$-invariant differential operators, and ${mathcal D}^-$ its subring of negative degree operators. We prove that $Mmapsto M^{ann}= {operatorname Ann}_{mathcal D^-}(M)$ defines an isomorphism between the category of ${mathcal D}$-submodules of $B$ and a category of modules formed as lowest weight spaces. This is applied to a construction of simple ${mathcal D}$-submodules of $B$ when $G$ is a generalized symmetric group, to show that $B^{ann}$ is a so-called Gelfand model. Using differential algebra and lowest weight methods we also prove branching rules, entailing the main results in the representation theory of the symmetric group, such as a differential construction of the Young basis." @default.
- W2246382146 created "2016-06-24" @default.
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- W2246382146 date "2015-06-20" @default.
- W2246382146 modified "2023-10-16" @default.
- W2246382146 title "Decomposition of modules over invariant differential operators" @default.
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