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arXiv · 2405.06158

An example of the Jantzen filtration of a D-module

Simon Bohun·Anna Romanov
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Abstract

We compute the Jantzen filtration of a D-module on the flag variety of $\mathrm{SL}_2(\mathbb{C})$. At each step in the computation, we illustrate the $\mathfrak{sl}_2(\mathbb{C})$-module structure on global sections to give an algebraic picture of this geometric computation. We conclude by showing that the Jantzen filtration on the D-module agrees with the algebraic Jantzen filtration on its global sections, demonstrating a famous theorem of Beilinson--Bernstein.

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Simon Bohun, Anna Romanov. 2024-05-10. An example of the Jantzen filtration of a D-module. https://doi.org/10.1017/s1446788724000168

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