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Lie Theory and Geometry(Progress in Mathematics Vol.123) hardcover XLIII, 596 p. 94

Brylinski, Jean-Luc, Brylinski, Ranee, Guillemin, Victor, Kac, Victor 　編

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価格 \45,095（税込）

発行年月	1994年11月
出版社／提供元	Birkhauser Boston
出版国	アメリカ合衆国
言語	英語
媒体	冊子
装丁	hardcover
ページ数／巻数	XLIII, 596 p.
ジャンル	洋書／理工学／数学／解析学
ISBN	9780817637613
商品コード	0209441913
本の性格	学術書
商品URL	https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=0209441913

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.

Normality of Some Nilpotent Varieties and Cohomology of Line Bundles on the Cotangent Bundle of the Flag Variety.- Holomorphic Quantization and Unitary Representations of the Teichmüller Group.- Differential Operators on Conical Lagrangian Manifolds.- Groups and the Buckyball.- Spinor and Oscillator Representations of Quantum Groups.- Familles cohérentes sur les groupes de Lie semi-simples et restriction aux sous-groupes compacts maximaux.- The Differential Geometry of Fedosov’s Quantization.- Closedness of Star Products and Cohomologies.- The Algebra of Chern—Simons Classes, the Poisson Bracket on it and the Action of the Gauge Group.- A Distinguished Family of Unitary Representations for the Exceptional Groups of Real Rank = 4.- Reduced Phase Spaces and Riemann—Roch.- The Invariants of Degree up to 6 of all n-ary m-ics.- Tensor Products of Modules for a Vertex Operator Algebra and Vertex Tensor Categories.- Enveloping Algebras: Problems Old and New.- Integrable Highest Weight Modules Over Affine Superalgebras and Number Theory.- Quasi-Equivariant D-Modules, Equivariant Derived Category, and Representations of Reductive Lie Groups.- Meromorphic Monoidal Structures.- The Nil Hecke Ring and Singularity of Schubert Varieties.- Some Classical and Quantum Algebras.- Total Positivity in Reductive Groups.- The Spectrum of Certain Invariant Differential Operators Associated to a Hermitian Symmetric Space.- Compact Subvarieties in Flag Domains.