Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$
Abstract
We show that the cohomological Laplacian in degree 1 in the group cohomology of $\operatorname{SL}_3(\mathbb{Z})$ is a sum of hermitian squares in the algebra $\mathbb{M}_n(\mathbb{R}G)$. We provide an estimate of the spectral gap for this Laplacian for every unitary representation.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2022
- DOI:
- 10.48550/arXiv.2207.02783
- arXiv:
- arXiv:2207.02783
- Bibcode:
- 2022arXiv220702783K
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Operator Algebras