$L^2$-cohomology and deformations of the left regular representation

Christoph Gamm; Andreas Thom

$L^2$-cohomology and deformations of the left regular representation

Operator Algebras 2026-07-20 v1

Authors: Christoph Gamm , Andreas Thom

Abstract

We study deformations of unitary representations $\pi\colon G\to U(H)$ whose coefficients lie in the Hilbert-Schmidt ideal $HS(H)\subset B(H)$ . Interesting applications arise for the left-regular representation of surface groups and, more generally, cocompact lattices in the automorphism group of a Fuchsian building of conformal dimension $<2$ .

Keywords

L2-cohomology deformations left regular representation Hilbert-Schmidt surface groups Fuchsian buildings

Cite

@article{arxiv.2607.17670,
  title  = {$L^2$-cohomology and deformations of the left regular representation},
  author = {Christoph Gamm and Andreas Thom},
  journal= {arXiv preprint arXiv:2607.17670},
  year   = {2026}
}

Comments

16 pages, no figures