Harish-Chandra's admissibility problem for Banach space representations of $\mathrm{SL}(2,\mathbb{R})$

Francesca Astengo; Michael G. Cowling; Bianca Di Blasio

Harish-Chandra's admissibility problem for Banach space representations of $\mathrm{SL}(2,\mathbb{R})$

Representation Theory 2026-05-11 v3

Authors: Francesca Astengo , Michael G. Cowling , Bianca Di Blasio

Abstract

We show that irreducible strongly continuous representations of $\mathrm{SL}(2,\mathbb{R})$ on certain Banach spaces are admissible and that the admissibility of Banach space representations of SL(2,R) and the invariant subspace problem are intimately related.

Keywords

Harish-Chandra admissibility Banach space representations SL(2,R) irreducible representations invariant subspace problem

Cite

@article{arxiv.2406.12626,
  title  = {Harish-Chandra's admissibility problem for Banach space representations of $\mathrm{SL}(2,\mathbb{R})$},
  author = {Francesca Astengo and Michael G. Cowling and Bianca Di Blasio},
  journal= {arXiv preprint arXiv:2406.12626},
  year   = {2026}
}

Comments

15 pages, extensively revised to focus on general Banach spaces rather than on Hilbert spaces

Harish-Chandra's admissibility problem for Banach space representations of $\mathrm{SL}(2,\mathbb{R})$

Abstract

Keywords

Cite

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