{"abstract":[{"lang":"eng","text":"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."}],"publication":"arXiv:2605.18000","citation":{"ama":"Burban I, Drozd Y. Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R). <i>arXiv:260518000</i>. Published online 2026.","bibtex":"@article{Burban_Drozd_2026, title={Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R)}, journal={arXiv:2605.18000}, author={Burban, Igor and Drozd, Yuriy}, year={2026} }","mla":"Burban, Igor, and Yuriy Drozd. “Representation Theory of the Real Gelfand Order and Real Harish-Chandra Modules for SL_2(R).” <i>ArXiv:2605.18000</i>, 2026.","short":"I. Burban, Y. Drozd, ArXiv:2605.18000 (2026).","chicago":"Burban, Igor, and Yuriy Drozd. “Representation Theory of the Real Gelfand Order and Real Harish-Chandra Modules for SL_2(R).” <i>ArXiv:2605.18000</i>, 2026.","apa":"Burban, I., &#38; Drozd, Y. (2026). Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R). In <i>arXiv:2605.18000</i>.","ieee":"I. Burban and Y. Drozd, “Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R),” <i>arXiv:2605.18000</i>. 2026."},"type":"preprint","external_id":{"arxiv":["2605.18000"]},"date_created":"2026-07-07T06:22:32Z","date_updated":"2026-07-07T06:23:43Z","year":"2026","status":"public","title":"Representation theory of the real Gelfand order and real Harish-Chandra modules for SL_2(R)","author":[{"id":"72064","full_name":"Burban, Igor","last_name":"Burban","first_name":"Igor"},{"last_name":"Drozd","first_name":"Yuriy","full_name":"Drozd, Yuriy"}],"user_id":"72064","language":[{"iso":"eng"}],"_id":"66292"}