2002 Fiscal Year Final Research Report Summary
Irreducible unitary representation of non compact quantum group SUq(1,1) and its quantum symmetric space
Project/Area Number 
11440052

Research Category 
GrantinAid for Scientific Research (B)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Global analysis

Research Institution  University of Tsukuba 
Principal Investigator 
MASUDA Tetsuya Univ. of Tsukuba, Institute of Math., Ass. Prof. > 筑波大学, 数学系, 助教授 (70202314)

CoInvestigator(Kenkyūbuntansha) 
TAIRA Kazuaki University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (90016163)
KAJITANI Kunihiko University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (00026262)
TAKEUCHI Mitsuhiro University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (00015950)
KAKEHI Tomiyuki Univ. of Tsukuba, Institute of Math., Ass. Prof., 数学系, 助教授 (70231248)
MIYAMOTO Masahiko University of Tsukuba, Institute of Math., Prof., 数学系, 教授 (30125356)

Project Period (FY) 
1999 – 2002

Keywords  quantum group / symmetric space / computer system 
Research Abstract 
The target of this research had been put in such a high level so that we were not able to carry out all the projects on the occasion that we asked for this research grant. On the process of our research concerning the quantum symmetric space, we recognized a quantum 4dimensional spheres which are not realized as the quantum symmetric space, and we also succeeded to have an explicit construction of a quantum vector bundle on such spaces which are regarded to be very basic in the direction of quantum gauge theories leaving lots of problems to be studied in the future. Then, at the same time, we faced to compute the cyclic cohomologies of those quantum manifolds so that we decided to use a special type of computer system which had never tried to use for such a problem coming from pure mathematics due to the extremely huge amount of computations by hands. However, this problem of computer aided computation is still left together with the tunung of the computer system itself. On the other hand, a general framework to deal with the objects which are so called the locally compact quantum groups was eventually finished and already submitted to a journal in France. By making use of this framework, we are now ready to proceed in the direction of the very detailed study of the explicitly given examples of the quantum groups of the non compact type.

Research Products
(2 results)