An example of the Jantzen filtration of a D-module
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908371556237312 |
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| author | Bohun, Simon Romanov, Anna |
| author_facet | Bohun, Simon Romanov, Anna |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An example of the Jantzen filtration of a D-module Bohun, Simon Romanov, Anna Representation Theory Algebraic Geometry 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. |
| title | An example of the Jantzen filtration of a D-module |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2405.06158 |