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PreprintCC BY 4.0arXiv

Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group

  • Nikolay Nessonov
  • Nhok Tkhai Shon Ngo
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Abstract

In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of "block-diagonal" inductive limits of semidirect products 𝕋NrtimesSN of the compact N-dimensional torus 𝕋N with the symmetric group SN. The classification is proved by means of a variant of the ergodic method of Vershik and Kerov, namely by studying the weak limits of characters of finite-dimensional subgroups. As an application of our results, we give another proof of the classification of indecomposable characters of the infinite unitary group with block diagonal embeddings.

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Cite

BibTeXRIS
BibTeX
@misc{nessonov2026indecomposable,
  title = {{Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group}},
  author = {Nikolay Nessonov and Nhok Tkhai Shon Ngo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25275},
  eprint = {2609.25275},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25275},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group
AU  - Nikolay Nessonov
AU  - Nhok Tkhai Shon Ngo
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25275
UR  - https://arxiv.org/abs/2609.25275
AB  - In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of "block-diagonal" inductive limits of semidirect products 𝕋^NrtimesS_N of the compact N-dimensional torus 𝕋^N with the symmetric group S_N. The classification is proved by means of a variant of the ergodic method of Vershik and Kerov, namely by studying the weak limits of characters of finite-dimensional subgroups. As an application of our results, we give another proof of the classification of indecomposable characters of the infinite unitary group with block diagonal embeddings.
ER  -