On the intertwining differential operators for line bundles over real projective spaces

Toshihisa Kubo, Bent Ørsted

Published 2023-12-25Version 1

We classify and construct $SL(n,\mathbb{R})$-intertwining differential operators $\mathcal{D}$ for line bundles over real projective space $\mathbb{RP}^n$ 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 $\mathrm{Ker}(\mathcal{D})$ and image $\mathrm{Im}(\mathcal{D})$ of $\mathcal{D}$. The standardness of the homomorphisms $\varphi$ corresponding to the differential operators $\mathcal{D}$ between generalized Verma modules are also discussed.