---
_id: '66292'
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.
author:
- first_name: Igor
  full_name: Burban, Igor
  id: '72064'
  last_name: Burban
- first_name: Yuriy
  full_name: Drozd, Yuriy
  last_name: Drozd
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.
  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>.
  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} }'
  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.
  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.
  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).
date_created: 2026-07-07T06:22:32Z
date_updated: 2026-07-07T06:23:43Z
external_id:
  arxiv:
  - '2605.18000'
language:
- iso: eng
publication: arXiv:2605.18000
status: public
title: Representation theory of the real Gelfand order and real Harish-Chandra modules
  for SL_2(R)
type: preprint
user_id: '72064'
year: '2026'
...