2025/05/19 by Wei, Yunsong
Mathematics · #Advanced Algebra and Geometry #Affine variety #Algebraic Geometry and Number Theory #Algebraic cycle #Algebraic extension #Algebraic group #Algebraic surface #Dimension of an algebraic variety #FOS: Mathematics #Function field of an algebraic variety #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Reductive group #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Unipotent
paper · pdf · doi:10.48550/arxiv.2505.12755
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the invariant algebraic D-modules on an affine variety under the action of an algebraic group.For linear algebraic groups with the multiplication action by themselves, such D-modules correspond to representations of their Lie algebra. For unipotent algebraic groups, we show that two invariant D-modules are isomorphic if and only if they lie in the same fiber of the GIT (Geometric Invariant Theory) quotient of the space of representations under the action of conjugation. Additionally, we classify invariant D-modules over the algebraic torus and the Borel subgroup of the general linear group.