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

Yamane给出了仿射李超代数G的Serre型定理，即用Chevalley生成子表示G，并定义了它们所满足的关系。对于仿射量子化超代数U_qG，他也给出了类似的结果。他还用Drinfeld发生器给出了类型为a (M|N)^<(1)>的U_qG，并定义了它们所满足的关系，定义了它们所满足的关系。与非超级情况不同，定义关系非常复杂。然而，通过比较G与U_qG的定义关系，我们可以发现G的Verma模的权空间的维数与U_qG的权空间的维数是一致的。设R = C[s^<±1>,t^<±1>]为二元洛朗多项式环。设D为sl（2 bbb 2）的中心推广。然后dim D/sl(2|2) = 2。和D R (R) = D【积】【对称】Ω_R /博士是宇宙的中心延伸sl(2 | 2)【积】R .他给的D有限Chevalle (R) ... 更多y发电机和有限definig关系,也做了同样的事情为D型仿射谎言superalgebra D ^ < (1) > = D【积】C [t ^ <±1 >]+ Cc。很容易描述内核的自然地图D (R)→sl (2 | 2) (R)通过使用发电机。由此，我们也可以用有限的Chevalley生成函数和无限的定义关系给出sl(2 bb0 2)(R)的表示。Yamane给出了仿射李超代数G的Serre型定理，即用Chevalley生成子表示G，并定义了它们所满足的关系。对于仿射量子化超代数U_qG，他也给出了类似的结果。他还用Drinfeld发生器给出了类型为a (M|N)^<(1)>的U_qG，并定义了它们所满足的关系。与非超级情况不同，定义关系非常复杂。然而，通过比较G与U_qG的定义关系，我们可以发现G的Verma模的权空间的维数与U_qG的权空间的维数是重合的。设R = C[s^<±1>,t^<±1>]为二变量洛朗多项式环。设D为sl（2|2）的普适中心扩展。然后dim D|sl(2|2) = 2。和D R (R) = D【积】【对称】Ω_R /博士是宇宙的中心延长sl(2 | 2)【积】R .他给演讲有限D (R)的《李群发电机和有限的定义关系,同时也做了同样的事情的D型仿射谎言superalgebra D ^ < (1) > = D【积】C [t ^ <±1 >]+ Cc。很容易描述内核的自然地图D (R)→sl (2 | 2) (R)通过使用发电机。由此，我们也可以用有限的Chevalley生成函数和无限的定义关系给出sl(2 bb0 2)(R)的表示。Nagatomo发展了顶点算子代数的表示理论，并将其应用于共形场论中的问题。其中一个重要的结果是电荷共轭轨道模型的简单模的分类，这为研究中心电荷大于等于1的共形场理论开辟了一条道路。另一方面，他将相关函数的系统研究应用于模形式和准模形式的构造，引起了模形式理论工作者的广泛关注。少

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