Representation of superalgebras and their quantum groups

超代数及其量子群的表示

• 批准号: 08454009
• 负责人: WAKIMOTO Minoru
• 金额: $ 1.79万
• 依托单位: KYUSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08454009/
• 关键词: affine super algebra; super conformal algenbra; conformal-super algenbra; kertex operator algenbra; extension of representations; superconformal代数

In the research of this year, I found a new method to construct the N=2 superconformal algebra in terms of the affine superralgebras sl (2,1)^*. This construction has a very curious and interesting aspect ; namely in this construction, odd roots with length zero play an important role, and so the similar method does not work for usual (affine) Lie algebras. Further I extended this method to construct the N=4 superconformal algebra in terms of affine superalgebras. A paper containing these results is now in preparation.I made also some investigations and observations on the structure and representations of "conformal-superalgebras" , which are new algebraic structures, recently discovered by V.G,Kac, closely related to the super-conformal algebras. They have a great advantage that their calculation is much simpler and easier than that of the usual superconformal algebras or vertex operator algebras. Their representation theory, however, is quite different from that of superconformal algebras or even from that of usual simple Lie algebras, and we observe many curious phenominia in their representations. So their representation theory has its own interests in itself, and provides a lot of new problems which should be investigated. This year I made a joint research with V.G.Kac and S.-J.cheng on the extension of irreducible representations of conformal superalgebras, from which we can see that the representation of "conformal-superalgebras" is very rich.

在今年的研究中，我发现了一种用仿射超代数sl(2,1)^*构造N=2超共形代数的新方法。这个结构有一个非常奇怪和有趣的方面；也就是说，在这种构造中，长度为零的奇根起着重要的作用，因此类似的方法不适用于通常的（仿射）李代数。进一步将此方法推广到仿射超代数中构造N=4超共形代数。目前正在编写一份载有这些结果的文件。“共形超代数”是V.G，Kac最近发现的与超共形代数密切相关的新代数结构，我也对其结构和表示进行了一些研究和观察。与一般的超共形代数或顶点算子代数相比，它们的计算更简单、更容易，这是它们的一大优点。然而，它们的表示理论与超共形代数的表示理论甚至与通常的简单李代数的表示理论都有很大的不同，我们在它们的表示中观察到许多奇怪的现象。因此，他们的表征理论有其自身的利益，并提出了许多值得研究的新问题。今年我和V.G.Kac和s.j.做了一个联合研究。Cheng关于共形超代数的不可约表示的推广，从中可以看出“共形超代数”的表示是非常丰富的。

项目成果

T.Miyakawa: "On L^*l-Stability of Stationary Navier-Stokes Flows in R^*n" To be published in Journal of Math.Sciences, Univ.of Tokyo. (1997)

T.Miyakawa：“On L^*l-R^*n 中的稳态纳维-斯托克斯流的稳定性” 发表于东京大学数学科学杂志。

S.-J.Cheng: "On extensions of conformal modules" To be published in the Proceedings of cinference in “Topological Field Theory and Related Topics". (1997)

S.-J.Cheng：“论共角模的扩展”将发表在“拓扑场论及相关主题”的论文集上（1997）。

S.-J.Cheng: "On extensions of conformal modules" To be published in the proceedings of the conference on "Topological Field Fheory and Pelated Topics". (1997)

S.-J.Cheng：“论共形模的扩展” 将发表在“拓扑场理论和相关主题”会议论文集上。

A.Yoshikawa: "Mean values and mean-cenvolution products" Kyushu J.Math.Vol50 No.2. 385-436 (1996)

A.Yoshikawa：“平均值和平均重合乘积”九州 J.Math.Vol50 第 2 期。

A.Yoshikawa: "Mean values and mean-convolution products" Kyushu J.Math.Vol.50. 385-436 (1996)

A.Yoshikawa：“平均值和平均卷积积”九州 J.Math.Vol.50。