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PreprintarXiv licencearXiv

Representation theory of the real Gelfand order and real Harish-Chandra modules for SL2(ℝ)

  • Igor Burban
  • Yuriy Drozd
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Abstract

In this article we study the principal block of the category of real Harish-Chandra modules for the group SL2(RR) and relate it to the category of finite dimensional modules over the so-called real Gelfand order. We describe several distinguished classes of the corresponding indecomposable representations.

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Cite

BibTeXRIS
BibTeX
@misc{burban2026representation,
  title = {{Representation theory of the real Gelfand order and real Harish-Chandra modules for $\mathsfSL_2(\mathbbmR)$}},
  author = {Igor Burban and Yuriy Drozd},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.18000},
  eprint = {2605.18000},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.18000},
}
RIS
TY  - UNPB
TI  - Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(ℝ)
AU  - Igor Burban
AU  - Yuriy Drozd
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2605.18000
UR  - https://arxiv.org/abs/2605.18000
AB  - In this article we study the principal block of the category of real Harish-Chandra modules for the group SL_2(RR) and relate it to the category of finite dimensional modules over the so-called real Gelfand order. We describe several distinguished classes of the corresponding indecomposable representations.
ER  -