Representation of superalgebras and their quantum groups
Project/Area Number  08454009 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
Algebra

Research Institution  KYUSHU UNIVERSITY 
Principal Investigator 
WAKIMOTO Minoru Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (00028218)

CoInvestigator(Kenkyūbuntansha) 
KAWASHIMA Shuichi Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (70144631)
KUNITA Hiroshi Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (30022552)
YOSHIKAWA Atushi Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (80001866)
YAMADA Mieko Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (70130226)
MIYAKAWA Tetsuro Kyushu University, Graduate School of Mathematics, Professor, 大学院・数理学研究科, 教授 (10033929)

Project Fiscal Year 
1996 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1996 : ¥2,800,000 (Direct Cost : ¥2,800,000)

Keywords  affine super algebra / super conformal algenbra / conformalsuper algenbra / kertex operator algenbra / extension of representations / アフィン・スーパー・リー環 / super conformal代数 / conformalsuper代数 / 頂点作用素代数 / 表現のextension / superconformal代数 
Research Abstract 
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 "conformalsuperalgebras" , which are new algebraic structures, recently discovered by V.G,Kac, closely related to the superconformal 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 "conformalsuperalgebras" is very rich.

Report
(3results)
Research Output
(9results)