L²-cohomology and deformations of the left regular representation

2026/07/20 by Christoph Gamm, Andreas Thom
#math.OA

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Abstract

We study deformations of unitary representations π\colon G→ U(H) whose coefficients lie in the Hilbert-Schmidt ideal HS(H)⊂ 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.

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