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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.11023 |
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| _version_ | 1866917402110853120 |
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| author | Slipper, Aaron |
| author_facet | Slipper, Aaron |
| contents | We construct and compare three D-module models for the minimal representation of the conformal group of an even-dimensional quadratic space. Let $V$ be a quadratic space over a field $κ$ of characteristic $0$, let $C$ be the isotropic cone in $V^*$, and let $G$ be the conformal group of $V$. We prove an equivalence between the category of modules over the Grothendieck differential operator algebra $D_C$, a Kazhdan--Laumon glued category attached to the smooth locus of the cone, and a category of "harmonic" twisted D-modules on a flag variety $G/P$. Along the way, we construct a quadric Fourier transform on $D_C$, provide a geometric proof that the algebra $D_C$ is finitely generated despite the singularity of $C$, and explain the quasi-classical analogue of this minimal representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11023 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometrization of the Schrödinger Model for the Minimal Representation of an Even Orthogonal Group: The de Rham Setting Slipper, Aaron Representation Theory Number Theory Rings and Algebras We construct and compare three D-module models for the minimal representation of the conformal group of an even-dimensional quadratic space. Let $V$ be a quadratic space over a field $κ$ of characteristic $0$, let $C$ be the isotropic cone in $V^*$, and let $G$ be the conformal group of $V$. We prove an equivalence between the category of modules over the Grothendieck differential operator algebra $D_C$, a Kazhdan--Laumon glued category attached to the smooth locus of the cone, and a category of "harmonic" twisted D-modules on a flag variety $G/P$. Along the way, we construct a quadric Fourier transform on $D_C$, provide a geometric proof that the algebra $D_C$ is finitely generated despite the singularity of $C$, and explain the quasi-classical analogue of this minimal representation. |
| title | Geometrization of the Schrödinger Model for the Minimal Representation of an Even Orthogonal Group: The de Rham Setting |
| topic | Representation Theory Number Theory Rings and Algebras |
| url | https://arxiv.org/abs/2604.11023 |