Higher Specht polynomials and modules over the Weyl algebra

Ibrahim Nonkane; Leonard Todjihounde

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arXiv · 2110.06738

Higher Specht polynomials and modules over the Weyl algebra

Ibrahim Nonkane·Leonard Todjihounde

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Abstract

In this paper, we study an irreducible decomposition structure of the $\Dc$-module direct image $\pi_+(\Oc_{ \bC^n})$ for the finite map $\pi: \bC^n \to \bC^n/ ({\Sc_{n_1}\times \cdots \times \Sc_{n_r}}).$ We explicitly construct the simple component of $\pi_+(\Oc_{\bC^n})$ by providing their generators and their multiplicities. Using an equivalence of categories and the higher Specht polynomials, we describe a $\D$-module decomposition of the polynomial ring localized at the discriminant of $\pi$. Furthermore, we study the action invariants, differential operators, on the higher Specht polynomials.

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BibTeX RIS

Ibrahim Nonkane, Leonard Todjihounde. 2021-10-13. Higher Specht polynomials and modules over the Weyl algebra. https://arxiv.org/abs/2110.06738

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