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In [6], we proposed a method to construct a G-invariant exponential family on a homogeneous space G/H by using a representation of G. In this paper, we prove that for any G-invariant exponential family \(\mathcal {P}\) on G/H, we can construct a family \(\mathcal {P}_0\) by the method which satisfies \(\mathcal {P}\subset \mathcal {P}_0\) .

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Note on Harmonic Exponential Families on Homogeneous Spaces

  • 会议论文

  • 发表日期：

    2026年

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  • Koichi Tojo,
  • Taro Yoshino

摘要

In [6], we proposed a method to construct a G-invariant exponential family on a homogeneous space G/H by using a representation of G. In this paper, we prove that for any G-invariant exponential family \(\mathcal {P}\) on G/H, we can construct a family \(\mathcal {P}_0\) by the method which satisfies \(\mathcal {P}\subset \mathcal {P}_0\) .