2016 Fiscal Year Final Research Report
Constructions of analytic models of small representaions
| Project/Area Number |
26800052
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Ryukoku University (2016)
The University of Tokyo (2014-2015) |
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Principal Investigator |
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| Research Collaborator |
ØRSTED Bent
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | small representations / Torasso's representation / Verma modules / hypergeometric equations |
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| Outline of Final Research Achievements |
For this research program we have studied about realizations of small (infinite dimensional) representations in solution spaces to intertwining differential operators. Over the years we have succeeded realizing a number of small representations, one of which is called Torasso's representation. In 1983 Torasso constructed a genuine small representation by using a somewhat technical method; it requires a certain efforts to construct the representation. In contrast, in our method, one can easily construct the representation by solving a well-known ordinary differential equation (hypergeometric differential equation).
So far we have applied our method only to a particular Lie group. Nonetheless, as the technique itself is simple, it is likely that it can be applied to other real simple Lie groups. We are planning on pursuing our method for further study.
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| Free Research Field |
Lie群・Lie環の表現論
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