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arXiv · 2312.15621

On the intertwining differential operators from a line bundle to a vector bundle over the real projective space

Toshihisa Kubo·Bent Ørsted
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Abstract

We classify and construct $SL(n,\mathbb{R})$-intertwining differential operators $\mathcal{D}$ from a line bundle to a vector bundle over the real projective space $\mathbb{RP}^{n-1}$ by the F-method. This generalizes a classical result of Bol for $SL(2,\mathbb{R})$. Further, we classify the $K$-type formulas for the kernel $\text{Ker}(\mathcal{D})$ and image $\text{Im}(\mathcal{D})$ of $\mathcal{D}$. The standardness of the homomorphisms $\varphi$ corresponding to the differential operators $\mathcal{D}$ between generalized Verma modules are also discussed.

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Toshihisa Kubo, Bent Ørsted. 2023-12-25. On the intertwining differential operators from a line bundle to a vector bundle over the real projective space. https://arxiv.org/abs/2312.15621

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