An example of the Jantzen filtration of a D-module

2024/05/10 by Bohun, Simon, Romanov, Anna
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.06158

Abstract

We compute the Jantzen filtration of a D-module on the flag variety of SL₂(ℂ). At each step in the computation, we illustrate the \mathfraksl₂(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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• Two proofs of a Jantzen Conjecture for Whittaker Modules
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