English

Representation theory of the real Gelfand order and real Harish-Chandra modules for $\mathsf{SL}_2(\mathbbm{R})$

Representation Theory 2026-05-19 v1 Rings and Algebras

Abstract

In this article we study the principal block of the category of real Harish-Chandra modules for the group SL2(\RR)\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.

Keywords

Cite

@article{arxiv.2605.18000,
  title  = {Representation theory of the real Gelfand order and real Harish-Chandra modules for $\mathsf{SL}_2(\mathbbm{R})$},
  author = {Igor Burban and Yuriy Drozd},
  journal= {arXiv preprint arXiv:2605.18000},
  year   = {2026}
}