Geometric invariants of representations and the Whittaker models
表示的几何不变量和 Whittaker 模型
基本信息
- 批准号:15540183
- 负责人:
- 金额:$ 1.98万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2003
- 资助国家:日本
- 起止时间:2003 至 2005
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
During the research period, we obtain many results about the symmetry of commuting differential operators, which is relevant to the main subjects of this research, namely Whittaker models and invariants of representations.The completely integrable system called Calogero-Moser-Sutherland model (which we abbreviate as CMS model in the following of this abstract) is closely related to root systems and Weyl groups. The Hamiltonian operator of this model is invariant under the action of a Weyl group and the potential function of it is expressed by means of the corresponding root system. Note that the potential function of it possesses inverse square singularities along the walls of a Weyl chamber. We study the commutants of a Hamiltonian operator whose potential function possesses inverse square singularities along some hyperplanes passing through the origin. It is shown that the Weyl group symmetry of the potential function and the commutants naturally results from such singularities and the generic nature of the coupling constants. Moreover, we have obtained the following results :(1)If this symmetry is of the classical type, the potential function must be one of the known ones.(2)In the rank two cases, the potential function must satisfy some linear relations.(3)In the rank two cases, the order of the commutant is at least the number of singular lines.(4)Deformation of A_2 type CMS model is possible if and only if two of the coupling constants are 1.(5)Deformation of B_2 type CMS model is possible even if no coupling constant is 1.(6)A new deformation of the B_2 type CMS model is constructed.Besides the above investigation, we study an elementary method of constructing F_4 type invariant polynomials.
在研究期间,我们得到了许多关于交换微分算子对称性的结果,这些结果与本研究的主要主题--Whittaker模型和表示不变量有关。完全可积系统Calogero-Moser-Sutherland模型(以下简称CMS模型)与根系和Weyl群密切相关。该模型的哈密顿算符在Weyl群的作用下是不变的,其势函数用相应的根系表示。请注意,它的势函数沿Weyl腔壁具有反平方奇点。我们研究了哈密顿算子的交换子,它的势函数沿着通过原点的一些超平面具有反平方奇性。结果表明,势函数和交换子的Weyl群对称性是由这种奇点和耦合常数的一般性质自然产生的。此外,我们还得到了以下结果:(1)如果这种对称性是经典类型的,则势函数一定是已知的。(2)在二阶情形下,势函数一定满足某种线性关系。(3)在二阶情形下,(4)当且仅当两个耦合常数为1时,A_2型CMS模型才可能发生形变。(5)即使没有耦合常数为1时,B_2型CMS模型也可能发生形变。(6)构造了B_2型CMS模型的新形变。
项目成果
期刊论文数量(44)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Askey-Wilson integrals associated with root systems
与根系统相关的 Askey-Wilson 积分
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:Kenji TNIGUCHI;Tomomi KAWAMURA;Kenji TANIGUCHI;Tomomi KAWAMURA;Masahiko ITO;Masahiko ITO;Masahiko ITO;Tomomi KAWAMURA;Masahiko ITO
- 通讯作者:Masahiko ITO
Links associated with beneric immersions of graphs
与图表的贝尼里克沉浸相关的链接
- DOI:
- 发表时间:2004
- 期刊:
- 影响因子:0
- 作者:Kazuhiko Aomoto;Masahiko Ito;Kenji Taniguchi;Tomomi Kawamura
- 通讯作者:Tomomi Kawamura
q-difference shift for a BC_n-type Jackson integral arising from 'elementary' symmetric polynomials
由“基本”对称多项式产生的 BC_n 型 Jackson 积分的 q 差分位移
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:Kazuhiko Aomoto;Masahiko Ito;Kenji Taniguchi;Tomomi Kawamura;Kenji TANIGUCHI;Tomomi KAWAMURA;Kenji Taniguchi;Masahiko Ito;Masahiko Ito;Masahiko ITO;Masahiko ITO;谷口 健二;Masahiko Ito;Masahiko Ito;Masahiko Ito
- 通讯作者:Masahiko Ito
Links and gordian numbers associated with certain generic immersions of circles
与某些通用的圆圈沉浸相关的链接和重要数字
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:Kenji TNIGUCHI;Tomomi KAWAMURA;Kenji TANIGUCHI;Tomomi KAWAMURA;Masahiko ITO;Masahiko ITO;Masahiko ITO;Tomomi KAWAMURA;Masahiko ITO;Masahiko ITO;Tomomi KAWAMURA
- 通讯作者:Tomomi KAWAMURA
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
TANIGUCHI Kenji其他文献
STORM SURGE SIMULATION IN THE TOKYO BAY UNDER FUTURE CLIMATE CONDITIONS USING PSEUDO GLOBAL WARMING METHOD
使用伪全球变暖方法模拟未来气候条件下东京湾风暴潮
- DOI:
10.2208/kaigan.74.i_613 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
TANIGUCHI Kenji;SANUKI Hiroshi;SHIBUO Yoshihiro;TAJIMA Yoshimitsu - 通讯作者:
TAJIMA Yoshimitsu
Study on Probabilistic Inundation Hazard along the Coast of South Pacific Islands: Case Study at Lakeba Island in Fiji
南太平洋岛屿沿岸洪水灾害概率研究——以斐济拉克巴岛为例
- DOI:
10.2208/kaigan.76.2_i_1231 - 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
TAJIMA Yoshimitsu;SHOJI Takumi;TANIGUCHI Kenji - 通讯作者:
TANIGUCHI Kenji
狩野川台風のバリエーションに基づく東京湾の高潮と浸水範囲におよぼす気候変動の感度評価
基于鹿川台风变化的气候变化对东京湾风暴潮和淹没区的敏感性评估
- DOI:
- 发表时间:
2017 - 期刊:
- 影响因子:0
- 作者:
TANIGUCHI Kenji;SANUKI Hiroshi;SHIBUO Yoshihiro;TAJIMA Yoshimitsu;澁谷容子・森 信人・金 洙列・中條壮大・間瀬 肇 - 通讯作者:
澁谷容子・森 信人・金 洙列・中條壮大・間瀬 肇
TANIGUCHI Kenji的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('TANIGUCHI Kenji', 18)}}的其他基金
The origin of the cultivated Chrisanthemum
栽培菊花的起源
- 批准号:
23580008 - 财政年份:2011
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Development of integrated data assimilation technique by using satellite and X-band MP Radar observation
利用卫星和X波段MP雷达观测综合资料同化技术的发展
- 批准号:
22686045 - 财政年份:2010
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Young Scientists (A)
Development of cloud microphysics data assimilation system with integrated use of multiple satellite observation products
多卫星观测产品集成云微物理数据同化系统开发
- 批准号:
20760323 - 财政年份:2008
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Young Scientists (B)
Construction and classification of systems of multi-variable commutative differential operators
多变量交换微分算子系统的构造与分类
- 批准号:
19540226 - 财政年份:2007
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
STUDIES ON QUANTUM EFFECT DEVICE MODELING BASED ON DEVICE STRUCTURE AND FUNCTIONAL CIRCUITS
基于器件结构和功能电路的量子效应器件建模研究
- 批准号:
08455167 - 财政年份:1996
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Research on Functional Devices Utilizing Single Electron Tunneling Phenomena
利用单电子隧道现象的功能器件研究
- 批准号:
05452188 - 财政年份:1993
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for General Scientific Research (B)
Study of Random Telegraph Noise in Ultra Small MOSFET and its Reliability
超小型MOSFET随机电报噪声及其可靠性研究
- 批准号:
01550248 - 财政年份:1989
- 资助金额:
$ 1.98万 - 项目类别:
Grant-in-Aid for General Scientific Research (C)