Spectral gap for the cohomological Laplacian of SL₃(ℤ)

2022/07/06 by Kaluba, Marek, Mizerka, Piotr, Nowak, Piotr W. · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2207.02783

Abstract

We show that the cohomological Laplacian in degree 1 in the group cohomology of SL₃(ℤ) is a sum of hermitian squares in the algebra \mathbbM_n(ℝG). We provide an estimate of the spectral gap for this Laplacian for every unitary representation.

Cited by

• Inducing spectral gaps for the cohomological Laplacians of Sp_2n(ℤ)

Related

• Inducing spectral gaps for the cohomological Laplacians of SL_n(ℤ) and SAut(F_n)
• Inducing spectral gaps for the cohomological Laplacians of Sp_2n(ℤ)
• Kazhdan's Property (T) via Semidefinite Optimization
• Spectral theory of automorphic forms and analysis of invariant operators on SL₃(\calZ with applications
• Proof of Lew's conjecture on the spectral gaps of simplicial complexes