论文标题
$ \ operatorname {sl} _3（\ Mathbb {z}）$的共同体学Laplacian的光谱差距
Spectral gap for the cohomological Laplacian of $\operatorname{SL}_3(\mathbb{Z})$
论文作者
论文摘要
我们表明，在$ \ peripatorname {sl} _3（\ mathbb {z}）$的群体共同体中，学位1中的共同体学拉普拉斯$是代数$ \ mathbb {m Mathbb {m} _n（mathbb {m} _n（\ mathbb {\ mathbb {\ mathbb {r r} g）$ {mathbbbb $ \ mathbb $ \ mathbb {mathbb {z}）$的总和。我们为每种单一表示的Laplacian提供了光谱差距的估计。
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.
