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res:
bibo_abstract:
- 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 $U$.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Joachim
foaf_name: Hilgert, Joachim
foaf_surname: Hilgert
foaf_workInfoHomepage: http://www.librecat.org/personId=220
- foaf_Person:
foaf_givenName: Thomas
foaf_name: Baier, Thomas
foaf_surname: Baier
- foaf_Person:
foaf_givenName: Jose
foaf_name: Mourao, Jose
foaf_surname: Mourao
- foaf_Person:
foaf_givenName: Joao
foaf_name: Nunes, Joao
foaf_surname: Nunes
- foaf_Person:
foaf_givenName: Ana Christina
foaf_name: Ferreira, Ana Christina
foaf_surname: Ferreira
dct_date: 2024^xs_gYear
dct_language: eng
dct_title: Fibering polarizations and Mabuchi rays on symmetric spaces of compact
type@
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