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AN EXAMPLE OF THE JANTZEN FILTRATION OF A D-MODULE
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- Journal:
- Journal of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 11 November 2024, pp. 1-32
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We compute the Jantzen filtration of a
$\mathcal {D}$-module on the flag variety of 
$\operatorname {\mathrm {SL}}_2(\mathbb {C})$. 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 
$\mathcal {D}$-module agrees with the algebraic Jantzen filtration on its global sections, demonstrating a famous theorem of Beilinson and Bernstein.
