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15th Oka Symposium
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$B%?%$%H%k!'(BQuantization of Hitchin Spectral Curves and
Holomorphic Lagrangians
$B%"%V%9%H%i%/%H!'(BThe non-Abelian Hodge correspondence is a
diffeomorphism between the moduli space of stable G-Higgs
bundles on a compact Riemann surface C of genus greater
than 1, and the space of irreducible characters of the
fundamental group of C in G-representations. Here, G is
a complex simple Lie group. These two spaces have distinct
complex structures and are never biholomorphic. Recently,
a canonical biholomorphic map between particular holomorphic
Lagrangians, one on each side, is discovered (arXiv:1607.02172),
solving a conjecture of the physicist Davide Giotto.
In our solution, Kostant's "principal Three-Dimensional Subgroup$B!I(B
of 1959, and "opers" of Beilinson and Drinfeld, play a crucial
role. Apparently, Kostant's TDS is responsible for quantization
of Hitchin spectral curves as opers. In this talk, I will explain
this process of quantization from the holomorphic point of view.
The talk is based on my joint work with Olivia Dumitrescu.
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Phone: 0742-20-3361, <a class="moz-txt-link-abbreviated" href="mailto:e-mail:matsuzawa@cc.nara-wu.ac.jp">e-mail:matsuzawa@cc.nara-wu.ac.jp</a>
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