| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
The first theme of the project was to understand, by employing a suitable group action, the mysterious derivation/determination of geodesics on multivariate normal models given by Erisken in 1987. This was completely achieved by Hiroto Inoue, a PhD course student under my supervision. Actually, he proved that the normal model can be realized as a submanifold of a certain (pre-conjectured) Riemannian symmetric space (cone) by Riemann submersion and the mysterious derivation of geodesic follows from this fact. This result may provide a new understanding for the elliptical models including normal models. The second is expanding the representation theoretic study of α-determinant, which was originally defined in the framework of statistical and probability theory, we explored the group-subgroup determinant theory. Moreover, as the third theme, we obtain the fundamental results of multivariate Meixner-Pollaczek polynomials in the framework of harmonic analysis on Hermite symmetric spaces.
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