Representation theory of the quantized enveloping algebras and the quantized enveloping superalgebras

量化包络代数和量化包络超代数的表示论

基本信息

批准号：
10640022
负责人：
YAMANE Hiroyuki
金额：
$ 2.05万
依托单位：
Osaka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2001
项目状态：
已结题

项目摘要

Yamane gave a Serre type theorem for the affine Lie superalgebras G, namely he gave a presentation of G by the Chevalley generators and defining relations satisfied by them. He also gave a similar result for the affine quantised superalgebras U_qG. He alos gave a a presentation of U_qG of type A(M|N)^<(1)> by the Drinfeld generators and defining relations satisfied by them, and defining relations satisfied by them. Dnlike the non-super case, the defining relations are very complicate. However, by comparing the defining relations of G with the ones of U_qG, we can find out the coincidense of the dimensions of the weight sapaces of the Verma modules of G with the ones of U_qG. Let R = C[s^<±1>,t^<±1>] be the two variable Laurent polynomials ring. Let D be the universal central extention of sl(2|2). Then dim D/sl(2|2) = 2., and D(R) = D 【cross product】 R 【symmetry】 Ω_R/dR is the universal central extention of sl(2|2) 【cross product】 R. He gave a presentation of D(R) by the finite Chevalle … More y generators and finite definig relations, and also did the same thing for the D type affine Lie superalgebra D^<(1)> = D 【cross product】 C[t^<±1>] + Cc. It is easy to describe the kernel of the natural map D(R)→ sl(2|2)(R) by using the generators. By the fact, we can also give a presentation of sl(2|2)(R) by the finite Chevalley generators and infinite definig relations.Yamane gave a Serre type theorem for the affine Lie superalgebras G, namely he gave a presentation of G by the Chevalley generators and defining relations satisfied by them. He also gave a similar result for the affine quantised superalgebras U_qG. He alos gave a a presentation of U_qG of type A(M|N)^<(1)> by the Drinfeld generators and defining relations satisfied by them. Unlike the non-super case, the defining relations are very complicate. However, by comparing the defining relations of G with the ones of U_qG, we can find out the coincidence of the dimensions of the weight sapaces of the Verma modules of G with the ones of U_qG. Let R = C[s^<±1>,t^<±1>] be the two variable Laurent polynomial ring. Let D be the universal central extension of sl(2|2). Then dim D|sl(2|2) = 2., and D(R) = D 【cross product】 R 【symmetry】 Ω_R/dR is the universal central extension of sl(2|2) 【cross product】 R. He gave a presentation of D(R) by the finite Chevalley generators and finite defining relations, and also did the same thing for the D type affine Lie superalgebra D^<(1)> = D 【cross product】 C[t^<±1>] + Cc. It is easy to describe the kernel of the natural map D(R) → sl(2|2)(R) by using the generators. By the fact, we can also give a presentation of sl(2|2)(R) by the finite Chevalley generators and infinite defining relations.Nagatomo has developed the representation theory of vertex operator algebras, and has applied it to problems arising from conformal field theory. One of the important results is the classification of simple modules for the charge conjugation orbifold model, which opened a way to study conformal field theories with central charge more than or equal to one. On the other hand he applied the systematic study for correlation functions to a construction of modular forms and quasi-modular forms, which attracts much attention of those who work on the theory of modular forms. Less

Yamane给出了一个静脉内的Superalgebras G的塞雷类型理论，即，他由Chevalley Generators介绍G，并定义了他们满足的关系。他还为仿射量化的超级U_QG给出了类似的结果。 ALOS由Drinfeld Generators介绍了A（m | n）^<（1）>的U_QG，并定义了他们所满足的关系，并定义了他们所满足的关系。 DNICE否则，定义关系非常复杂。但是，通过将G与U_QG的定义关系进行比较，我们可以找出G的Verma模块重量间距的巧合与U_QG的u_qg。令r = c [s^<±1>，t^<±1>]为两个可变的laurent多项式环。令D为SL（2 | 2）的通用中心范围。然后dim d/sl（2 | 2）= 2，而d（r）= d [跨产品] r [对称]ω_r/dr是sl（2 | 2）[跨产品]的通用中心范围。 C [T^<±1>] + CC。使用发电机可以很容易地描述自然图D（R）→SL（2 | 2）（R）的内核。事实上，我们还可以通过有限的Chevalley Generator和无限的定义关系对SL（2 | 2）（r）的介绍。Yamane给出了一个serre类型的理论，以介绍了offine lie superalgebras g，即他给出了Chevalley Generators的G介绍G，并确定了他们满足的关系。他还为仿射量化的超级U_QG给出了类似的结果。 Alos由Drinfeld Generators介绍了A（M | N）^<（1）>的U_QG，并介绍了它们所满足的定义关系。与非少案件不同，定义关系非常复杂。但是，通过将G与U_QG的定义关系进行比较，我们可以找出G的Verma模块的重量间距的巧合与U_QG的u_qg。令r = c [s^<±1>，t^<±1>]为两个可变的laurent多项式环。令D为SL（2 | 2）的通用中心扩展。然后dim d | sl（2 | 2）= 2，而d（r）=d【跨产品] r [对称]ω_r/dr是Sl（2 | 2）[跨产品] R的通用中心扩展。 C [T^<±1>] + CC。使用发电机可以很容易地描述自然图D（R）→SL（2 | 2）（R）的内核。事实上，我们还可以通过有限的Chevalley发电机和无限定义关系对SL（2 | 2）（r）的介绍。NAGATOMO开发了Vertex Operator代数的表示理论，并将其应用于由整形型领域理论引起的问题。重要的结果之一是对电荷共轭Orbifold模型的简单模块的分类，该模块开辟了一种研究中心电荷超过或等于一个的保形场理论的方法。另一方面，他将系统研究应用于模块化形式和准模块化形式的构造，这吸引了那些从事模块化形式理论的人的关注。较少的