Geometry and Harmonic Analysis on Nilpotent Orbits
幂零轨道的几何与调和分析
基本信息
- 批准号:13440046
- 负责人:
- 金额:$ 5.12万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (B)
- 财政年份:2001
- 资助国家:日本
- 起止时间:2001 至 2004
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
(1)We describe the theta lifting of nilpotent orbits in the terms of invariant theory, and prove that (the closures of) some good liftings are normal variety and the action of the algebraic groups on them are multiplicity free. We also obtain a degree formula of the nilpotent orbits expressed by integrals.A general theory of the lifting of coherent sheaves are constructed, and in particular we prove the preservation of the multiplicities of the support of coherent sheaves.(2)For the indefinite unitary group U(p,p), we completely classify the spherical nilpotent orbits and at the same time we describe the structure of the function rings on them.(3) We generalize the notion of theta lifting to general orbits other than nilpotent ones, and shed a light on the research of the complete understanding of the orbit correspondence. This includes an example of the unimodular congruence classes of the bilinear forms studied by Sekiguchi, Djokovic, Zhao.At last, we summarize the research of each investigator.Sekiguchi has studied the unimodular congruence classes of the bilinear forms from the view point of the invariant theory.Ohta has clarified the correspondence between the orbits of complex reductive algebraic groups and its real forms.More generally, he extends his research to the orbits of symmetric pairs.Yamashita has investigated the relations between associated cycles of the unitary representations of semisimple Lie groups, their isotropy representations and generalized Whittaker vectors.
(1)We用不变量理论描述了幂零轨道的θ提升,证明了一些好的提升的闭包是正规簇,代数群在它们上的作用是多重自由的.得到了用积分表示的幂零轨道的度公式,构造了相干层提升的一般理论,特别证明了相干层支撑重数的保持性.(2)对于不定酉群U(p,p),我们对球面幂零轨道进行了完全分类,并给出了球面幂零轨道上函数环的结构。(3)我们将θ提升的概念推广到一般轨道而不是幂零轨道,从而为轨道对应的完整理解研究提供了一个思路。最后,我们总结了各位学者的研究成果:关口从不变论的角度研究了双线性型的幺模同余类,太田阐明了复约化代数群的轨道与其真实的形式之间的对应关系,Yamashita将他的研究扩展到对称对的轨道。Yamashita研究了半单李群的酉表示、它们的各向同性表示和广义Whittaker向量的相关圈之间的关系。
项目成果
期刊论文数量(68)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Theta lifting of unitary lowest weight modules and their associated cycles
单一最低重量模块的 Theta 提升及其相关循环
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:K.Nishiyama;Zhu;Chen-bo
- 通讯作者:Chen-bo
関口次郎: "The closure ordering of adjoint nilpoteuforlits in so (p, q)"Tohoku Math. J. (2). 53巻. 395-442 (2001)
Jiro Sekiguchi:“so (p, q) 中伴随 nilpoteuforlits 的闭包排序”Tohoku Math J. (2)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Theta lifting of nilpotnet orbits for symmetric pairs.
对称对的尼尔波特网轨道的 Theta 提升。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:Kyo Nishiyama
- 通讯作者:Kyo Nishiyama
藤井道彦: "On strang convergence of hyperbolic 3-cone-manifolds whose singular sets have uniformly thick fabular neighborhoods"J. Math. Kyoto Univ.. 41巻2号. 421-428 (2001)
藤井道彦:“关于具有均匀厚神话邻域的双曲 3 锥流形的奇异收敛”,京都大学数学杂志,第 41 卷,第 2 期,421-428(2001 年)
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
A note on affine quotients and equivariant double fibrations
关于仿射商和等变双纤维的注释
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:Junya Satoh;K.Nishiyama
- 通讯作者:K.Nishiyama
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NISHIYAMA Kyo其他文献
NISHIYAMA Kyo的其他文献
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{{ truncateString('NISHIYAMA Kyo', 18)}}的其他基金
Orbits on flag varieties and moment maps
旗帜品种和矩图上的轨道
- 批准号:
21340006 - 财政年份:2009
- 资助金额:
$ 5.12万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Affine quotient maps and invariant differential operators
仿射商图和不变微分算子
- 批准号:
17340037 - 财政年份:2005
- 资助金额:
$ 5.12万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Theta correspondence and associated cycles
Theta 对应和相关周期
- 批准号:
11640025 - 财政年份:1999
- 资助金额:
$ 5.12万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Lie algebra of differential oeprators on algebraic variety and its representations
代数簇微分算子的李代数及其表示
- 批准号:
09640030 - 财政年份:1997
- 资助金额:
$ 5.12万 - 项目类别:
Grant-in-Aid for Scientific Research (C)