---
res:
  bibo_abstract:
  - In 1970, Gelfand posed the problem of classifying the indecomposable objects in
    a representation category equivalent to the principal block of Harish-Chandra
    modules for $\mathsf{SL}_2(\mathbb{R})$; explicit solutions were obtained by Bondarenko,
    and, independently, Crawley-Boevey. In this article, we give a complete answer
    to Gelfand's problem from a derived category perspective. We classify indecomposable
    objects in the bounded derived category of nilpotent representations of the Gelfand
    quiver in terms of band and string complexes, and determine their images under
    the derived Auslander-Reiten translation, the sign involution, and the contragredient
    duality. The four main combinatorial classes are characterized in Lie-theoretic
    as well as homological terms. For the abelian category of nilpotent representations,
    we provide projective resolutions, standard homological invariants and explicit
    representation matrices of all indecomposables. Our approach can be extended to
    arrow ideal completions of path algebras of skew-gentle quivers.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Igor
      foaf_name: Burban, Igor
      foaf_surname: Burban
      foaf_workInfoHomepage: http://www.librecat.org/personId=72064
  - foaf_Person:
      foaf_givenName: Wassilij
      foaf_name: Gnedin, Wassilij
      foaf_surname: Gnedin
  dct_date: 2026^xs_gYear
  dct_language: eng
  dct_title: Representation theory of the Gelfand quiver and Harish-Chandra modules
    for SL_2(R)@
...