preprint
Fibering polarizations and Mabuchi rays on symmetric spaces of compact type
Joachim
Hilgert
author 220
Thomas
Baier
author
Jose
Mourao
author
Joao
Nunes
author
Ana Christina
Ferreira
author
In this paper, we describe holomorphic quantizations of the cotangent bundle of a symmetric space of compact type $T^*(U/K)\cong U_\mathbb{C}/K_\mathbb{C}$, along Mabuchi rays of $U$-invariant Kähler structures. At infinite geodesic time, the Kähler polarizations converge to a mixed polarization $\mathcal{P}_\infty$. We show how a generalized coherent state transform relates the quantizations along the Mabuchi geodesics such that holomorphic sections converge, as geodesic time goes to infinity, to distributional $\mathcal{P}_\infty$-polarized sections. Unlike in the case of $T^*U$, the gCST mapping from the Hilbert space of vertically polarized sections are not asymptotically unitary due to the appearance of representation dependent factors associated to the isotypical decomposition for the $U$-action. In agreement with the general program outlined in [Bai+23], we also describe how the quantization in the limit polarization $\mathcal{P}_\infty$ is given by the direct sum of the quantizations for all the symplectic reductions relative to the invariant torus action associated to the Hamiltonian action of $U$.
2024
eng
arxiv
@article{Hilgert_Baier_Mourao_Nunes_Ferreira_2024, title={Fibering polarizations and Mabuchi rays on symmetric spaces of compact type}, journal={arxiv}, author={Hilgert, Joachim and Baier, Thomas and Mourao, Jose and Nunes, Joao and Ferreira, Ana Christina}, year={2024} }
Hilgert, J., Baier, T., Mourao, J., Nunes, J., & Ferreira, A. C. (2024). Fibering polarizations and Mabuchi rays on symmetric spaces of compact type. In <i>arxiv</i>.
Hilgert, Joachim, et al. “Fibering Polarizations and Mabuchi Rays on Symmetric Spaces of Compact Type.” <i>Arxiv</i>, 2024.
Hilgert J, Baier T, Mourao J, Nunes J, Ferreira AC. Fibering polarizations and Mabuchi rays on symmetric spaces of compact type. <i>arxiv</i>. Published online 2024.
Hilgert, Joachim, Thomas Baier, Jose Mourao, Joao Nunes, and Ana Christina Ferreira. “Fibering Polarizations and Mabuchi Rays on Symmetric Spaces of Compact Type.” <i>Arxiv</i>, 2024.
J. Hilgert, T. Baier, J. Mourao, J. Nunes, and A. C. Ferreira, “Fibering polarizations and Mabuchi rays on symmetric spaces of compact type,” <i>arxiv</i>. 2024.
J. Hilgert, T. Baier, J. Mourao, J. Nunes, A.C. Ferreira, Arxiv (2024).
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