Lie Theory and Geometry(Progress in Mathematics Vol.123) hardcover XLIII, 596 p. 94
Brylinski, Jean-Luc,
Brylinski, Ranee,
Guillemin, Victor,
Kac, Victor
編
発行年月 |
1994年11月 |
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出版国 |
アメリカ合衆国 |
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言語 |
英語 |
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媒体 |
冊子 |
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装丁 |
hardcover |
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ページ数/巻数 |
XLIII, 596 p. |
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ジャンル |
洋書/理工学/数学/解析学 |
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ISBN |
9780817637613 |
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商品コード |
0209441913 |
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本の性格 |
学術書 |
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商品URL
| https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=0209441913 |
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内容
given there. The Symposium, entitled "Lie Theory, Algebra and Geomet ric Quantization", seems to be a fitting descriptive synthesis of Kostant's works. This summary was prepared by the Editors. We thank David Vogan for giving us his account of Kostant's work in representation theory up to the mid 1970s. Any inaccuracies are of course the responsibility of the Editors. 50s Some of Kostant's first papers ([1] [4] [5]) are devoted to a study of the holonomy groups of homogeneous spaces. Kostant described the Lie al gebra of the holonomy group in terms of certain operators Ax associated with Killing fields X. In [4] and [5] the holonomy group is described for a large class of homogeneous spaces. In [10] Kostant gives a characteri zation of those affine connections which admit locally a transitive group of connection preserving transformations. These results are reproduced in the treatise of Kobayashi and Nomizu. In [3] it is proved that for any Rie mannian metric on the sphere sn, the holonomy group is always the full rotation group. This basic result is derived from a representation-theoretic fact proved in [10], namely, that if a subgroup G of SO(n) (for n ~ 5) has no invariants in I\i jRn for all 0 < i < n, then G = SO(n). Kostant gave in [2] a complete classification of real Cartan subalgebras of a real simple Lie algebra.