Project/Area Number  09640019 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  Hitotsubashi University 
Principal Investigator 
YAMADA Hiromichi Graduate School of Economics, Prof., 大学院・経済学研究科, 教授 (50134888)

CoInvestigator(Kenkyūbuntansha) 
ISHIMURA Naoyuki Hitotsubashi University, Graduate School of Economics, Assoc.Prof., 大学院・経済学研究科, 助教授 (80212934)
YAMAZAKI Masao Hitotsubashi University, Graduate School of Economics, Assoc.Prof., 大学院・経済学研究科, 助教授 (20174659)
MACHIDA Hajime Hitotsubashi University, Faculty of Commerce, Prof., 商学部, 教授 (40090534)
IWASAKI Shiro Hitotsubashi University, Graduate School of Economics, Prof., 大学院・経済学研究科, 教授 (00001842)
永島 孝 一橋大学, 大学院・経済学研究科, 教授 (00017526)
FUJITA Takahiko Hitotsubashi University, Faculty of Commerce, Prof., 商学部, 教授 (50144316)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  vertex operator algebra / Virasoro algebra / conformal element / finite group / simple module / 頂点作用素代数 / ヴィラソロ代数 / 共形元 / 有限群 / 既約表現 
Research Abstract 
In 1997 a subalgebra having order three symmetry of a vertex operator algebra associated with a rank two root lattice of type A was discovered and its properties were studied. In particular its automorphism group was determined and its simple modules were classified. The results were written in a joint paper Ternary codes and vertex operator algebras. Relations between this vertex operator algebra and the Monster module still remain to be studied. Moreover, Borwein type identity was studied from a point of view of vertex operator algebra. The results were written in a joint paper Borwein identity and vertex opertor algebras. In 1998 all highest weight vectors with weight at most two of a vertex operator algebra associated with a root lattice of type A were classified. Highest weight vectors are important, because once they are known then a vertex operator algebra can be decomposed into a direct sum of simple modules for a tensor product of Virasoro vertex operator algebras. Although not all highest weight vectors are known, much information about the structure of the vertex operator algebra can be obtained from highest weight vectors with weight at most two. For example, a vertex operator algebra having a symmetry of order 4 was constructed by using these highest weight vectors. Recently all highest weight vectors were classified in the case of rank three root lattice of type A.In order to generalize this result to a root lattice of arbitrary rank, a new idea would be required.
