权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Completely integrable systema and representation theory of infinite dimen-sional algebras

无限维代数的完全可积系统和表示论

基本信息

批准号：
09440014
负责人：
DATE Etsuro
金额：
$ 9.15万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440014/
关键词：
Onsager algebra nilpotent Lie algebras Schur function Schrodinger operator semilinear elliptic equation vertex operator algebra L operators A^<(1)>_1 principal realization 完全積分可能系可解リー環巾零リー環

项目摘要

In a collaboration with Professor S.S.Roan of Academia Sinica (Taipei), the head investigator of this research project has determined the structure of quotient of the Onsager algebra by ideals of it in the case when the quotients do not have central elements. This almost determines the structure of quotients of the Onsager algebra. In particular the case not determined in the previous researches are fixed by finding a relation with the project of classifying nilpotent Lie algebras by classifying the ideals in the nilpotent part of Kac-Moody Lie algebras. To find such relationship computer algebra system on a workstation was very helpful and indispensable, especially in computing examples. The Onsager algebra can be viewed as a Lie algebra deformation of the nilpotent part of the affine Lie algebra A^<(1)>_1. If we identify A^<(1)>_1 with a central extension of the current algebra, the Onsager algebra is a fixed point set of an involution. By using this presentation we can study the structures of ideals of the Onsager algebra. In order to fix the remining case, we used the principal (twisted) realization of A^<(1)>_1. We think that this kind of principal realization will play some important role in the study of deformation of nilpotent parts of other affine Lie algebras in connection with conformal field theory. We are preparing manuscript on this result. Other investigators in this research project have obtained new results in the study of spectrum of one dimensional Schrodinger operator with a random potential, an identity involving Schur functions, positive solutions of sernilinear elliptic partial differential equations, classification of irreducible representations of vertex operator algebras related with free fermions, relationship of L operators in quantum inverse scattering method and Drinfeld's genarators in affine quantum enveloping algebras and other areas.

本研究项目的首席研究员与台北中央研究院的roan教授合作，在商没有中心元素的情况下，通过对商的理想确定了Onsager代数商的结构。这几乎决定了Onsager代数的商的结构。特别是通过对Kac-Moody李代数的幂零部分的理想进行分类，找到与幂零李代数分类方案的关系，解决了以往研究中未确定的情况。在计算机代数系统中找到这种关系是非常有用的，尤其是在计算实例中。Onsager代数可以看作是仿射李代数a ^<(1)>_1的幂零部分的李代数变形。如果我们用当前代数的中心扩展来识别A^<(1)>_1，则Onsager代数是一个对合的不动点集。利用这一表述，我们可以研究Onsager代数的理想结构。为了解决这个问题，我们使用了A^<(1)>_1的主（扭曲）实现。我们认为这种主实现将对其他仿射李代数的幂零部的变形与共形场论相联系的研究起到一定的作用。我们正在准备这一结果的手稿。本研究项目的其他研究者在一维随机势薛定谔算子的谱、涉及舒尔函数的恒等式、半线性椭圆型偏微分方程的正解、与自由费米子相关的顶点算子代数的不可约表示的分类、量子逆散射法中的L算子与仿射量子包络代数等领域的Drinfeld发生器的关系。