Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2602.14864 |
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Inhaltsangabe:
- Let $G/K$ be a Hermitian symmetric space and $V_τ$ an irreducible representation of $K$. We study the ring $\mathcal D^G(G/K, V_τ)$ of $G$-invariant differential operators on sections of vector bundles $G\times_{(K, τ)} V_τ$ over $G/K$ defined by a finite-dimensional representation $(V_τ, τ)$ of $K$. We classify irreducible representations $(V_τ, τ)$ such that $\mathcal D^G(G/K, V_τ)$ is commutative. We construct eigenfunctions for the differential operators and study the invariance property of the eigenvalues under the Weyl group for the restricted real root system of $G$.