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- W4384643896 abstract "A compact Kahler manifold $left( M,omega ,Jright) $ with $T$-symmetry admits a natural mixed polarization $mathcal{P}_{mathrm{mix}}$ whose real directions come from the $T$-action. In cite{LW1}, we constructed a one-parameter family of Kahler structures $left( omega ,J_{t}right) $'s with the same underlying Ka hler form $omega $ and $J_{0}=J$, such that (i) there is a $T$-equivariant biholomorphism between $left( M,J_{0}right) $ and $left( M,J_{t}right) $ and (ii) Kahler polarizations $mathcal{P} _{t}$'s corresponding to $J_{t}$'s converge to $mathcal{P}_{mathrm{mix}}$ as $t$ goes to infinity. In this paper, we study the quantum analog of above results. Assume $L$ is a pre-quantum line bundle on $left( M,omega right) $. Let $mathcal{H}_{t}$ and $ mathcal{H}_{mathrm{mix}}$ be quantum spaces defined using polarizations $mathcal{P}_{t}$ and $mathcal{P}_{mathrm{mix}}$ respectively. In particular, $mathcal{H}_{t}=H_{bar{partial}_{t}}^{0}left( M,Lright) $. They are both representations of $T$. We show that (i) there is a $T$-equivariant isomorphism between $mathcal{H}_{0}$ and $mathcal{H}_{mathrm{mix}}$ and (ii) for regular $T$-weight $lambda $, corresponding $lambda $-weight spaces $ mathcal{H}_{t,lambda }$'s converge to $mathcal{H}_{mathrm{mix},lambda }$ as $t$ goes to infinity." @default.
- W4384643896 created "2023-07-19" @default.
- W4384643896 creator A5058380236 @default.
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- W4384643896 date "2023-07-15" @default.
- W4384643896 modified "2023-09-25" @default.
- W4384643896 title "Limit of geometric quantizations on Kahler manifolds with T-symmetry" @default.
- W4384643896 doi "https://doi.org/10.48550/arxiv.2307.07759" @default.
- W4384643896 hasPublicationYear "2023" @default.
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