Year: 2024
Type: article
Abstract: 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.
Authors: SIMON BOHUN, ANNA ROMANOV
Institutions: University of Utah, UNSW Sydney
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: University of New South Wales
OpenAlex ID: W4404251251