Representation theory of the real Gelfand order and real Harish-Chandra modules for $\mathsf{SL}_2(\mathbbm{R})$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917507720282112 |
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| author | Burban, Igor Drozd, Yuriy |
| author_facet | Burban, Igor Drozd, Yuriy |
| contents | In this article we study the principal block of the category of real Harish-Chandra modules for the group $\mathsf{SL}_2(\RR)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18000 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Representation theory of the real Gelfand order and real Harish-Chandra modules for $\mathsf{SL}_2(\mathbbm{R})$ Burban, Igor Drozd, Yuriy Representation Theory Rings and Algebras In this article we study the principal block of the category of real Harish-Chandra modules for the group $\mathsf{SL}_2(\RR)$ 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. |
| title | Representation theory of the real Gelfand order and real Harish-Chandra modules for $\mathsf{SL}_2(\mathbbm{R})$ |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2605.18000 |