A new development of studies on stochastic process, statistical distributions and representation theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610006
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyushu University
• Principal Investigator: Wakayama Masato 九州大学, 学内共同利用施設等, 教授 (40201149)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 群作用 / 統計（情報）多様体 / Meixner-Pollaczek過程 / α行列式 / 正規分布モデル / 群行列式 / 対称錘

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.

Free Research Field

表現論