Pushforward measures on homogeneous spaces of non-unimodular groups and properties of modular functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929467640774656 |
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| author | Satomi, Takashi |
| author_facet | Satomi, Takashi |
| contents | This paper shows that a formula for the pushforward measures on the fiber bundle $ G \to G / H $ of homogeneous space of locally compact groups $ G $ and $ H $ can be written down by using the modular functions. As a result, we obtain the equality \begin{align} \frac{ Δ_G ( h ) }{ Δ_{ G / N } ( h N ) } = \frac{ Δ_H ( h ) }{ Δ_{ H / N } ( h N ) } \end{align} on the modular functions for any closed subgroups $ N $ and $ H $ of a locally compact group $ G $ with $ N \lhd G $ and $ N \subset H \subset G $ and any $ h \in H $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pushforward measures on homogeneous spaces of non-unimodular groups and properties of modular functions Satomi, Takashi Group Theory Classical Analysis and ODEs Functional Analysis General Topology 28C10 (Primary) 22D15, 43A85, 46G12, 54C35 (Secondary) This paper shows that a formula for the pushforward measures on the fiber bundle $ G \to G / H $ of homogeneous space of locally compact groups $ G $ and $ H $ can be written down by using the modular functions. As a result, we obtain the equality \begin{align} \frac{ Δ_G ( h ) }{ Δ_{ G / N } ( h N ) } = \frac{ Δ_H ( h ) }{ Δ_{ H / N } ( h N ) } \end{align} on the modular functions for any closed subgroups $ N $ and $ H $ of a locally compact group $ G $ with $ N \lhd G $ and $ N \subset H \subset G $ and any $ h \in H $. |
| title | Pushforward measures on homogeneous spaces of non-unimodular groups and properties of modular functions |
| topic | Group Theory Classical Analysis and ODEs Functional Analysis General Topology 28C10 (Primary) 22D15, 43A85, 46G12, 54C35 (Secondary) |
| url | https://arxiv.org/abs/2407.00670 |