{"title":"Fibering polarizations and Mabuchi rays on symmetric spaces of compact type","citation":{"chicago":"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.","mla":"Hilgert, Joachim, et al. “Fibering Polarizations and Mabuchi Rays on Symmetric Spaces of Compact Type.” <i>Arxiv</i>, 2024.","bibtex":"@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} }","apa":"Hilgert, J., Baier, T., Mourao, J., Nunes, J., &#38; Ferreira, A. C. (2024). Fibering polarizations and Mabuchi rays on symmetric spaces of compact type. In <i>arxiv</i>.","ieee":"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.","short":"J. Hilgert, T. Baier, J. Mourao, J. Nunes, A.C. Ferreira, Arxiv (2024).","ama":"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."},"user_id":"220","publication":"arxiv","date_created":"2024-08-08T07:16:05Z","type":"preprint","_id":"55565","abstract":[{"lang":"eng","text":"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 $U$."}],"status":"public","year":"2024","language":[{"iso":"eng"}],"date_updated":"2024-08-08T08:08:37Z","author":[{"full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim","last_name":"Hilgert"},{"full_name":"Baier, Thomas","last_name":"Baier","first_name":"Thomas"},{"last_name":"Mourao","first_name":"Jose","full_name":"Mourao, Jose"},{"full_name":"Nunes, Joao","last_name":"Nunes","first_name":"Joao"},{"last_name":"Ferreira","first_name":"Ana Christina","full_name":"Ferreira, Ana Christina"}]}