Pseudo-parabolic category over quaternionic projective plane

Abstract

Quaternionic projective plane $\mathbb{H}{P}^2$ is the next simplest conjugacy class of the symplectic group $SP(6)$ with pseudo-Levi stabilizer subgroup after the sphere ${\mathbb{S}}^4\simeq \mathbb{H}{P}^1$. Its quantization gives rise to a module category ${\mathcal{O}}_t\left(\mathbb{H}{P}^2\right)$ over finite-dimensional representations of $U_q(\mathfrak{sp}(6))$, a full subcategory in the category $\mathcal{O}$. We prove that ${\mathcal{O}}_t\left(\mathbb{H}{P}^2\right)$ is semi-simple and equaivalent to the category of quantized equivariant vector bundles on $\mathbb{H}{P}^2$.

arXiv comment27 pages. A revision of the previous version with improved presentation and more content added. Original results unchanged