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Coadjoint orbits of Sternberg type and their geometric quantization
 Coadjoint orbits of Sternberg type and their geometric quantization 教师介绍 本讲教师：孟国武 所属学科：理科 人　　气：276 课程介绍 摘要：Let \$kge 1\$ be an integer and \$mu\$ be the half of a {it nonzero} integer. The following statements hold for the elliptic co-adjoint orbit of the real Lie algebra \$mathfrak{so}(2, 2k+2)\$ that corresponds to the dominant weight \$(underbrace{|mu|, ldots, |mu|}_{k+1}, mu)\$. 1. This orbit is diffeomorphic to \$mathrm{SO}_0(2, 2k+2)/mathrm{U}(1, k+1)\$. As a result, it is pre-quantizable. 2. This orbit is the total space of a fiber bundle with base space being the total cotangent space of the punctured euclidean space of dimension \$2k+1\$ and the fiber being diffeomorphic to \$mathrm{SO}(2n)/mathrm{U}(n)\$. As a result, it admits a canonical polarization. 3. The geometric quantization of this orbit with its canonical polarization yields the Hilbert of square integrable sections of a Hermitian vector bundle over the punctured Euclidean space in dimension \$2k+1\$; moreover, this Hilbert space provides a geometric realization for the unitary highest weight \$frak{so}(2, 2k+2)\$-module with highest weight [(-k-|mu|, underbrace{ |mu|, ldots, |mu|}_k, mu).] The above results in Lie theory is obtained from the study of magnetized Kepler models in dimension \$2k+1\$.

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