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研究生： 徐健哲
Chien-Che Hsu
論文名稱： On Orbit Correspondence of General Linear Groups over R or C
實係數和複係數一般線性群的軌道對應
指導教授： 潘戍衍
Shu-Yen Pan
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2008
畢業學年度： 96
語文別： 英文
論文頁數： 38
中文關鍵詞： 冪零軌道 、軌道對應
外文關鍵詞： nilpotent orbit, orbit correspondence, reductive dual pair
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    • Let F = R or C. Let V, W be two finite-dimensional vector
    spaces over F. Let gl(V), gl(W) be the general linear algebras of two spaces, respectively. Let X be the tensor
    product of V and W over F.
    Let f: X♁X* -> gl(V) and g: X♁X* -> gl(W) be two moment maps and let cl(O) denotes the Zariski closure of the general linear group GL(V) in gl(V). In this article, we
    show that for a nilpotent orbit of GL(V) in gl(V) such that O is contained in the image of f, there is a unique orbit Q such that g{f^(-1)[cl(O)]} = cl(Q).

    1. An introduction to Lie Algebra 1.1 The notion of Lie algebra 1.2 Lie algebra and homomorphism 2. Some Preliminary Settings 2.1 Vector space isomorphism 2.2 Construction of a symplectic form 2.3 Three identifications under embedding 2.4 Two surjections indeced by the above embeddings 2.5 Identification of g with g* through trace form 3. The Relation between Nilpotent Orbits and Partitons 3.1 Nilpotent Orbits and Partitions 3.2 Zariski closure ordering 3.3 Some examples of complex nilpotent orbits correspondence (for detail, see the paper in pdf format.)

    [AM 89] M.F. Atiyah and L.G. Macdonald, Introduction to
    commutative algebra, Addition-Wesley Publishing Company,Inc., 1989.
    (for detail, please see the paper in pdf format.)

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